Let $X, Y$ have a joint uniform distribution on the unit square.
Thus,
$$f_{X\mid Y}(x\mid y) =
\begin{cases} 1 &0\leq x\leq1 \\
0 & \text{otherwise}
\end{cases}$$
Given $Y=y, X$ is Uniform$(0,1)$. We can write this as $X|Y=y∼$Uniform$(0,1)$.
How did it derive $$f_{X\mid Y}(x\mid y) = \begin{cases} 1 &0\leq x\leq1 \\ 0 & \text{otherwise} \end{cases}$$ And how did we get $X|Y=y∼$Uniform$(0,1)$?