P(A given B')=[P(A)-P(AnB)]/[1-P(B)].
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Prob(A given B) = Prob(A and B)/Prob(B)
Define your event as [A occurs and B does not occur] or as [A occurs and B' occurs] where B' is the complement of B. Equivalently, this is the event that [A and B' both occur].
P(A given B')=[P(A)-P(AnB)]/[1-P(B)].In words: Probability of A given B compliment is equal to the Probability of A minus the Probability of A intersect B, divided by 1 minus the probability of B.
P(A|B)= P(A n B) / P(B) P(A n B) = probability of both A and B happening to check for independence you see if P(A|B) = P(B)
The probability of the complement of an event, i.e. of the event not happening, is 1 minus the probability of the event.