I think we must use conditional probability, that is the integral of p(X|A)P(A), for example probability the prior event was 5 minutes ago probabity(the next o

I think we must use conditional probability, that is the integral of p(X|A)P(A), for example probability the prior event was 5 minutes ago probabity(the next one is 10 minutes from the previous one (that is 1/2). This is like markov chain, probability of next state depends of current state.