I'm not sure if I'm phrasing this correctly, but here goes:
If I have 10 events {a1,a2....a,10} , for example, and I know that on average each event has a success rate of {P1....P10} . These events are not independent.
If I want to figure out how event a2 affects the success of event a1, how would i go about doing this? Note that not all events are equally likely to happen, and if some event happens it's highly likely that some other event will not happen. And the success rates are an average over a large range of experiments, where each event is not equally likely to be represented.
How would I figure out the relation between events? What additional data would make this easier to figure out?
Not sure if this is what you are looking for, but there is a formula for conditional probability. It is written as
$P(A_2|A_1) = \frac{P(A_1∩A_2)}{P(A_1)}$
Where the probability of event $A_2$ happening given event $A_1$ happened is equal to the probability of the intersection of events $A_1$ and $A_2$over the probability of event $A_1$.
Is this what you are looking for in terms of a relationship between them?