Let $X_1$ and $X_2$ be two random variables uniformly distributed on $(0, 1)$. It is easy to calculate the distribution of minimum and maximum of these two numbers:
$$ P[\max(X_1, X_2)<x] = x^2 $$
$$ P[\min(X_1, X_2)<x] = 1 - P[\min(X_1, X_2)>x] \\ = 1 - (1-x)^2 = 2x-x^2 $$
But what would be the distribution of the minimum, given that the maximum is given and equal to some number $z$, i.e.
$$ P[\min(X_1, X_2)<x | \max(X_1, X_2)=z] = ? $$