Hmmm... I'm afraid I don't really understand your problem. I was hoping that looking at one of the proofs would give me a clue as to what you were missing, but it didn't.

The symbol p(A|B) is normally defined as p(AB)/p(B). What we need to check is that this matches up with our intuitive notion of conditional probability. Different people don't always have the same intuitive notions of probability, and the line that wikipedia takes is that probabilities conditional on B should be the probabilities you get when you set the chance of elementary events inconsi... (read more)