jmc

The point $(x,y)$ satisfies $x<y$ if and only if it belongs to the shaded triangle bounded by the lines $x=y$, $y=1$, and $x=0$, the area of which is 1/2. The ratio of the area of the triangle to the area of the rectangle is $\frac{1/2}{4}=\boxed{\frac{1}{8}}$.