You may have heard of the atheist advertising campaign in the U.K. headed up by noted atheist author and science popularizer Richard Dawkins. A group of atheists headlined by Dawkins purchased advertisements for the sides of London city buses which say, "There's probably no God. Now stop worrying and enjoy your life." This was supposedly a reaction against religious ads on buses which some atheists found objectionable.
The case raises many interesting issues. For one thing, it's interesting that a group of atheists says there's "probably" no God. The traditional definition of atheism was that it was the belief that there is no God, not that there is "probably" no God. In other words, an atheist under this definition wouldn't say there is "probably" no God, but that there is no God, period. It would be like defining a theist as someone who would say there "probably" is a God, rather than that there just IS a God. The fuzzy middle was occupied by what were called agnostics. These would be people who would say they don't know if there is a God, even though they would likely act in practice as if there were no God. Some would hold the position that you shouldn't believe in God unless there is indisputable proof that God exists.
Contemporary skeptics now frequently take the position that atheism is simply the absence of belief in God, rather than the presence of disbelief in God. Under this definition, anyone who lacks belief in God is an atheist. It's an interesting move, because it virtually eliminates the category of agnostic altogether. You don't have to hold the belief that there is no God to qualify as an atheist, you just have to not hold the belief that there is a God. Some who call themselves atheists actually argue passionately that this just is the definition of an atheist, and that anyone who thinks otherwise is an idiot (atheists, I've noticed, like to call other people idiots. In my experience they do this more than any other self-identified group. But that's another story).
The next issue is how Dawkins and his fellow atheists determined the probability of God's non-existence. One of the basic principles of probability theory is that you go from the known to the unknown. Say, for example, I want to determine the probability that I will be struck by lightning. I can start by finding out how many people get struck by lightning in a given population size, divide by the total population, and come up with a probability that any one person will be struck by lightning. But this really doesn't tell me if in fact I will be struck by lightning or not. Even though it's highly improbable that any one person will be struck by lightning, it still happens to some people.
So how does one calculate the probability of whether or not there is a God? After all, we know that some people will get struck by lightning. But when Dawkins and company say there "probably" is no God, they mean something different than if they were to say, "you probably won't be struck by lightning." They don't have a calculation to show that out of X number of possible universes there are Y number of gods, so therefore in our universe there probably is no God. What they really mean is "we don't think there is a God", or that the statement "there is a God" is likely false. This is a statement of opinion rather than of fact. If I say, "you probably won't be struck by lightning", that is a matter of fact that can be mathematically demonstrated. This makes the use of the word "probably" in the atheist ad somewhat misleading. This is especially so since Dawkins is a scientist and probability has a specific meaning in science and philosophy which is different than the meaning in the bus ad. It would be more accurate for the ad to say, "we don't think there is a God", but such an ad would doubtless be even less persuasive than the existing one. It's interesting to note that you may be struck by lightning anyways in spite of the low probability. It's likewise true that the statement, "there probably is no God" leaves open the possibility that, even from their standpoint, there might be a God. They just find it unlikely.
Going back to the question of why this group find the existence of God to be unlikely, we know for starters that Dawkins believes that there are good and complete naturalistic explanations for everything, and that therefore God is not necessary as an explanation for anything. Traditionally God has been appealed to as the explanation for various phenomena, but no longer. Science has made rapid and impressive progress in many areas over the last few centuries, so God is now out of a job, so to speak. It's still possible that there is a God, but there's no need to appeal to him as an explanation for anything in the observable universe.
But is that really true? Are there good and complete naturalistic explanations for everything in the universe? Dawkins (along with many others, of course) believes that Darwinian evolution fully accounts for the biological diversity on this planet. This is important to keep in mind, because some people mistakenly believe that evolution seeks to account for life in general. It does not. Darwin's theory (and its successors such as the neo-Darwinian synthesis and others) only seeks to explain the origin of species. It does not explain the origin of life itself. Nor does it explain the origin of the universe or the origin of consciousness (though some have made brave attempts at this latter). In fact there are no widely accepted naturalistic explanations for these phenomena, and there may be growing doubts about the adequacy of Darwinian evolution to even explain biological diversity. There are certainly many holes in Darwinian theory which have yet to be resolved in spite of the oft-heard pronouncement that "evolution is a fact."
But the belief that science will ultimately provide a naturalistic explanation for everything is nothing more than a statement of faith. Specifically, it's a statement of faith in two things: first, that nature really is all that there is, and second, that science will eventually explain it all. Both of these propositions are, in fact, highly implausible, and the second is almost certainly false. More importantly, neither of these statements are provable. It's impossible to prove that nature is all that there is unless one were to possess literally all knowledge. But no finite being could ever know that it possesses all knowledge. Only a being with infinite knowledge (such as God) could ever possess all knowledge and know that it possesses all knowledge. Thus naturalism can really never be proven. The second statement, that science will eventually explain everything, is almost certainly false. First, there are empirical limits on the ability of science to explain everything. These limits can be found in things like quantum theory and chaos theory just to give two examples. There's also Gödel's incompleteness theorem in mathematics which, when applied to physics, shows that science can't explain everything even in principle. So naturalism is every bit as much a statement of faith as theism or any other belief system. Moreover, it has the decided weakness of not being nearly as good an explanation for the observable properties of the universe as theism. The statement "there probably is no God" rests on highly dubious foundations.
But the final issue this ad raises is the conclusion: "Now stop worrying and enjoy your life." It's a strange conclusion in some ways. It would be as if I were to say, "when you die you're going to cease to exist and that will be the end of you, so don't worry about it!" That seems to be a probable cause to worry, rather than giving me cause not to. Presumably Dawkins and company mean to say that you shouldn't worry about things like judgment and life after death though their ad doesn't specify that. But again, this seems rather one-sided as it replaces one set of worries with another. A universe with no God is very different than a universe with a God, and I see no reason why a God-less universe is one in which there are fewer reasons to worry. On the contrary, belief in God also typically includes a belief that life is ultimately meaningful and purposeful, that injustices will ultimately be made right, and that goodness and truth will ultimately prevail. Not so with a God-less universe. If naturalism is true then justice or injustice (if those words have any real objective meaning at all) simply are, and that's the end of it. Ultimately it won't matter. People who have been treated unjustly in this life will die like dogs and cease to exist, with no hope of redress. It might be easy for an Oxford professor in a (relatively) free country like Great Britain to say "Now stop worrying and enjoy your life," but most of the world is not so privileged. Most of humanity has fared rather more poorly than that, and according to Dawkins's belief system, that's just too bad for them. Their lives were ultimately pointless anyhow. But to say to people like that "now stop worrying and enjoy your life" seems rather callous, not to mention nihilistic. It would be better to say, "now make the most of your ultimately meaningless and futile existence, you poor bugger!" But I suppose that wouldn't make for a very good bus advertisement, either!