You have two events a and b such that p(a|b) = 0.4 and p(a) = 0.4. based on this information, what can you conclude?

P(A|B) denotes the conditional probability. Which means the probability of event A given event B. In simple words, P(A|B) represents the probability of event A, considering that event B has already occurred.

Conditional probability also shows that the two events are dependent and probability of event B determines the probability of event A. 

If the conditional probability of A given B is equal to probability of event A, as given in question, this shows that event A is not affected by event B or the two event are not dependent because the probability of event A is same both in presence of event B and in absence of event B.