Random Variables X and Y follow a joint distribution:

Question

f(x,y)=(6-x-y)/8 if 0<x<2, 2<y<4
and 0, else
Find P(1<Y<3|X=1)

I first got the marginal distribution for x and got (3-x)/4 (Integrated from 2 to 4)and then got the conditional dist and got (5-y)/4 and then integrated that from 1 to 3 and got 1.5, which means it's wrong. What am I doing wrong?
Thanks