"I'm not going to put you in the Holding Cell for that, but only because I didn't actually ask the question you just went and answered."
"Yes. Though to state it more exactly, the right-hand side of the operator represents a starting set of worlds, such that we consider the probability of the left-hand side's event only within those worlds. We are not interested in the probability that a random Chelish citizen is a 5th-circle wizard; the total contribution there would be greater from INT 16s, or so it sounds like from what Carissa said. We're not interested in the probability that a random Chelish citizen is an INT 15 and becomes a 5th-circle wizard. We're interested in the probability that, if we select a random Chelish citizen, and then narrow our focus to only those worlds in which the random selection produced an INT 15, what is the chance within those worlds that the person becomes a 5th-circle wizard."
"Having assumed this fact away, it indeed becomes a premise for further deductions, as you say, just as if we were asking about whether it's valid that 'Y implies X' and for purposes of that validity are allowed to just assume Y is true. While asking about the probability that somebody becomes a 5th-circle wizard, conditional on INT 15, we have available the assumed fact of their INT 15-ness."