How can calculate conditional pdf of Y when you dont know about f(y)

Question

X is a uniform distribution on the interval (0,1). Y is a also uniform distribution on the interval (0,x). Its the only information that I could know. Then how can I calculate p(Y|x)? If you teach me, I will really appreciate that. Thanks for reading! Have a good day.

Answer 1

As the distribution of $Y$ is uniform, but dependent on $X$, the uniform PDF of $Y$ is actually $f_{Y|X} = \frac{1}{x}$ (as it is dependent on $X$).

Thus, $P(Y<y|X=x) = \int_0^y f_{Y|X}dy = \frac{y}{x}$