I have an answer to this question, but I'm not sure if my interpretation of the question is even right:
"In $n$ rolls of a fair die, let $X$ be the number of times 1 is rolled, and $Y$ the number of times 2 is rolled. Find the conditional distribution of $X$ given $Y = y$."
My answer: $$ P(X|Y) = \frac{P(X,Y)}{P(Y)}=\frac{P(X)P(Y)}{P(Y)}=P(X) $$
Fairly confident this is right but I always get confused at "find the distribution" questions...I'm always unsure I'm being asked for a pdf/pmf (obviously not in this case, but in other questions with more numbers I guess) or something else.