Consider a pair of random variables X, Y with constant joint density on the triangle with vertices

Question:

Consider a pair of random variables X, Y with constant joint density on the triangle with vertices at (0, 0), (3, 0), and (0, 3).
a. For 0 < y < 3, find the conditional density fX|Y (x | y) of X, given Y = y.
b. Find the conditional probability that X ≤ 1, given Y = 1.
c. Find the conditional probability that X ≤ 1, given Y ≤ 1.