If the probability that a certain event A occurs depends on the occurrence of an event B, than we speak of a conditional probability. Mathematically we write:
P(A|B) [1]
In the context of probabilistic causation we could speak of a "cause" if the probability that A occurs in case of the occurrence of B is greater than in the absence of B, or:
P(A|B)>P(A|~B) [2]
This formula suggests the definition of a negative cause:
P(A|B)<P(A|~B) [3]
A negative cause should be understand as an event which prevents or reduces the likelihood that another event occurs.
In case of:
P(A|B)=P(A|~B) [4]
we cannot speak of a "cause" in a meaningful sense, and have to conclude that A and B are independent.
