Relationship between joint probability distribution and causality?

I'm trying to interpret the results of some measurements in geophysics and thought this crowd might know the answer:

If a set of events A and B have a joint probability distribution P(A,B), how might this causality be described (in laymen English) between A and B from this joint probability?

If A and B have a joint expectation E(AB), how can causality be described from the elements of the matrix that can be written for each of the expected interactions A and B? [For instance, E(A_1B_1), E(A_2B_1), and so on]