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In conditional probability the question is: How does the probability of A change if we get additional information that B has occured?
If we are looking for a simple case where all the outcomes are equally likely. Then the probability of A is
P(A) = (number of outcomes corresponding to event A) / ( total number of outcomes)
The effect of this additional information is that we are interested only on those outcomes, which belong to the event B and so the probability is
P(A when B has occured) = (number of outcomes corresponding to event A and B) / ( total number of outcomes in B)
Using probabilities this can be expressed
P(A - B) = P(AB)/P(B).
P(A - B) denotes the probability that event A will occur given that event B has occurred already (A given B). The symbol - is a vertical line and does not imply division.

Provided P(B) > 0 we define the conditional probability of A given B as

P(A | B) = P(A ∩B) P(B) .