This I can grasp (and barely hold):

From a logical standpoint, Bayes’ rule makes a great deal of sense. If the evidence doesn’t match up with a hypothesis, I’m unlikely to believe it. On the other hand, if I think a hypothesis is extremely unlikely a priori, I’m also unlikely to believe it even if the evidence does appear to match up. For example, imagine that I have various hypotheses about the nature of a new-born baby of a friend of mine. If I’m presented with evidence in the form of a picture of a blond-haired baby girl, I’m likely to believe the baby is indeed a girl and does indeed have blond hair, and less likely to believe the baby is actually a brown-haired boy, since the evidence doesn’t agree with this hypothesis. On the other hand, if I’m presented with evidence of a picture of a baby dog, then I’m unlikely to believe the baby is actually a dog, since my prior belief in this hypothesis (that a human can give birth to a dog) is extremely small.

Now, when presented in the mathematical formula (which I can’t seem to copy and paste) it might as well be Klingon.