as usual this is incompete, are you conditioning on X,Y, X+Y....?
Since the binomial is finite and the Poissons are infinite, my guess is that you want X|X+Y or Y|X+Y
since these will be bounded
In any case use P(A|B)=P(AB)/P(B).
AND X+Y is Poisson.
A similar example can be found at the end of....http://mathworld.wolfram.com/BinomialDistribution.html
DO exactly what they did but at eq (66) use the Poisson and what I said about the sum of two indep Poissons.