Umm...I don't know how rigorous this explanation this is, but it might lead you in the right direction...because if you consider the Venn Diagram with probability spaces A and B, the probability space of A within B is given by the overlap of the two circles, or P(A∩B). Then you get the probability of landing in that space out of all the space in B...as in, the probability that if you choose circle B, you land in the overlap between A and B.

That's probably not what you were looking for, but hope it helps.