Bayes’s Theorem tells us how to revise our beliefs in light of new evidence. It looks like this:
P(B|A) x P(C|A.B) P(B|A.C) = ----------------- P(C|A)
This theorem can be used to test how the probability of a hypothesis H is affected given some evidence E for it. In this case we reformulate it thusly (K which stands for “background knowledge” is omitted for the sake of simplicity):
P(E|H) P(H|E) = P(H) x ------ P(E)
P(H) is called prior probability or probability without taking E into account. We don’t care what it is exactly; the theorem merely reports whether learning of E makes H more or less probable than before. P(E|H) is called likelihood or the probability that E would obtain given H; P(E) is called expectedness; and P(H|E) is called posterior probability or the probability after the evidence has come in. The less we expect E or, put differently, the more we are surprised by E, the greater the chance that H|E will hold. Since we tailor the hypothesis to fit the evidence, P(E|H) is often 1 or close to 1.
Let in our case H = theism, and E = desire for God. We are interested in finding out whether E is a good argument for H. It seems that P(desire for God | theism) is fairly high, because it is not unreasonable to expect that we would long for heaven if the Christian God exists. At the same time P(desire) is low, because God and heaven are certainly hidden from view, so much so that not everyone is convinced of their very existence. It is quite surprising that we long to transcend this world and ourselves. Surely, no non-human animal does so. Why on earth would we discover such a phenomenon within ourselves? One could try to develop some kind of an evolutionary story of how a desire for God has arisen in us, but any such attempt would be forced, in my view. Hence, P(H|E) > P(H), and thus E (desire) provides evidence or supports the case for theism.
Note again the limited ambition of this argument. It does not try to prove theism. Even if E is in fact excellent evidence for H, the prior P(H) can, for all we know, be very low, and even with the help of E, P(H|E) would still be low. Desire for God appears to be evidence in favor of theism; but there may be other arguments that weigh rather against it.