This is a follow up question with respect to the question here. Quickly summarising the question and the answer, if $X \sim U(0, S)$ and $Y \sim U(0, X)$, the joint cumulative probability distribution function in the case when $0 \leq y \leq x \leq S$ is given by $P(X \leq x, Y \leq y) = \frac{x}{S} + \frac{y}{S}(\ln x - \ln y)$.
I need the conditional probability $P(X < x | Y = y)$. I am unable to proceed thinking P(Y = y) is zero since it is point probability. How does one formulate this ?
Thanks in advacne.