Hey tangibleLime.

For P(Y|X) you will need to consider each slice of X (i.e. each value of x for X = x) and the distribution will still be a bi-variate distribution with four slices for each X=x. Just do it for a fixed x and then you will have a bi-variate distribution with a conditional distribution for P(Y=y) given a particular value of x observed (so four of these distributions).

For the second one you need to normalize this distribution by P(Y=y): Recall P(X=x|Y=y) = P(X=x and Y=y)/P(Y=y) so as an example P(X=3|Y=1) = P(X=3 and Y=1)/P(Y=1) = (1/8)/(1/2) = 1/4.