Uniform gap above a half given the sum is below one

Let $X$ and $Y$ be independent and uniform on $(0,1)$. Given that $X+Y<1$, what is the probability that $X-Y>\tfrac12$?

$\tfrac18$. Conditioned on $X+Y<1$, the point $(X,Y)$ is uniform on a triangle of area $\tfrac12$. The part with $x-y>\tfrac12$ is the small triangle with corners $(\tfrac12,0)$, $(1,0)$, $(\tfrac34,\tfrac14)$, of area $\tfrac1{16}$, and $\tfrac{1/16}{1/2}=\tfrac18$.