The latter. Here's Bayes:
P(A|B) = P(B|A)/PB P(A)
A and B are events. The blue part is usually called the likelihood ratio. The blue part is what Jabba thought he was asking for -- in his wording, "the Bayesian likelihood." In jt512's post, he calls it the "weight of evidence," which makes sense when you consider that when Bayes' theorem is used to drawn an inference, event B is usually data, or evidence, gleaned from the outside world. A is the event that a certain hypothesis is true. P(A) is the probability that your hypothesis is true, irrespective of what new evidence might tell you. The role of the blue part is to either attenuate or amplify the probability of your hypothesis based on how much worse or better it explains B, the evidence, over chance.