In statistics, the notation used to represent 'given that' - P(A|B) is the probability that event A happens given that event B happens. It is therefore defined as the number of times B intersects (is true as well as) A out of all the number of times A is true:
P(A|B) = P(A∩B)
P(A)
This notation is only used when the two events A and B are dependent on each other and do not directly influence the numbers, and the sum of the probabilities of A given that B is true, and A given that B is not true is equal to the probability of A. For example, if I took a ball out of a bag which had 3 amber balls in it and 3 blue balls, taking another ball out would be dependent on this first event but also numerically affected, so the above formula cannot be applied. However, if I chose a pupil at random from a group, with P(A) being the probability that she likes algebra and P(B) being the probability of her liking basketball, the formula could be applied.
If the two events were mutually exclusive, the formula cannot be used, since there is no intersection between the two events and P(A∩B) is equal to 0. It follows that P(A|B) is also equal to 0.
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