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.
Jabba didn't know what to call the blue part because statistics is not something he really knows much about. So he made up a word for it, "the Bayesian likelihood," and sprang it on people expecting them to just read his mind and know what he meant. (People who actually know a field and work in it use the standard language to avoid just such confusion.) Naturally you and I and everyone else thought he was asking for P(A|B), which can't be computed in his example without knowing P(A). If P(A|B) is the likelihood that a coin is two-headed given that it came up heads, we have to know P(A) -- the probability of a two-headed coin reckoned by a means other than the toss. For example, if you had a jar with 10 coins in it and were told that one of them is two-heaaded, you can draw a coin and use a series of tosses to home in on whether it's the two-headed one. But it would starte= with P(A)=0.1 for this particular case. P(A) might be different for a different reported (or estimated) population for two-headedness.
Jabba is trying to impress beyond his abilities. His present ability doesn't include the standard vocabulary of statistics, or the grasp of what those terms in the equation mean. There is a conceptual difference between a likelihood and a ratio of likelihoods. The latter is important in Bayes. We think of the blue term as a scaling factor that clusters around 1. If it works out to 1, then that tells us the evidence B is unrelated to the hypothesis A. Greater than 1 means the evidence favors the hypothesis. Less than 1 means it disfavors the hypothesis -- that the data B is actually evidence that the hypothesis A is not true. In order to get the likelihood P(B|A) to be in the neighborhood of 1, we normalize it using P(B), the probability that the data arose irrespective of any attempt to explain it.
Making up your own words for things that experts already have names for is a sign of bluffing. Additionally you may have noticed Jabba adopting words he sees in his critics' posts and using them in ways that suggest he doesn't really know what they mean. This is another symptom of the bluff. And lately, for example, you see him plastering the word "Bayesian" in front of everything, even when it makes no sense to qualify a concept that way. More bluff. He's arguing as if he really doesn't think any of his critics knows enough to rebut him confidently, and if he just throws around impressive-sounding terminology he can pretend he's been a genius.
