Conditional probability is used to find out the probability of some event happening given that some other event has happened. Easy right?
Therefore, conditional probability find that Y = y if X = x.
Formula: P(Y = y | X = x)
P(Y = y | X = x) = P(Y = y, X = x)/P(X = x)
Finally, a conditional probability is only defined when P(X = x) > 0.
What does that mean? Well, how can you compute a conditional probability if the event never happens? Answer is, you cannot.