I have calculated the probability that team A wont score a goal( using poisson distribution, with k=0, lambda = average goals scored)

I have calculated the probability that team B wont let a goal in ( using poisson distribution, with k=0, lambda = average goals let in)

I am trying to combine both, to give me the probability that team A wont score into team B.

I am getting very confused because event A and B are calculated independantly, but when I try to combine them, they are like 2 sides of the same event, since if A dont score, it automatically means that B dont let a goal in( i probably havent explained this very well)

although it would seem like I could use conditional probability, because I want to calculate probability that A dont score

**given that**B dont let a goal in, it doesnt work because P(A intersection B) is meaningless, because there is a total overlap between A and B

I have looked at all the other basic probability formula, for dependent events, independent events, P(A or B) etc, and nothing seems to apply.

Is there actually a solution here or am I looking at a non-problem, and if there is, where should I be looking?

thanks

neil