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

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.

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