Suppose X and Y are jointly continuous with joint density

f(x,y)= (exp(-x/y)*exp(-y))/y for 0<x<oo and 0<y<oo

f(x,y)= 0 otherwise

Find P(X>1|Y=y).

I first find the density functions of X and Y respectively.

But I am in difficulty in integrating (exp(-x/y)*exp(-y))/y with respect to y. Can someoneone provides some hints?

Also P(X>1|Y=y)=P(X>1 and Y=y)/P(Y=y)

But for continuous random variable Y, P(Y=y)=0?