P(A|B) denotes the probability of A, given B: out of all the "possible worlds" where B is true, in what proportion is A true? P(B) denotes the probability of B

P(A|B) denotes the probability of A, given B: out of all the "possible worlds" where B is true, in what proportion is A true? P(B) denotes the probability of B given no additional constraints: it's the same as saying P(B|true).