Let the distance between two points X and Y in (0, 1) be less than 1/3, which can be expressed as the absolute value of x-y < 1/3.

Then linear programming finds the absolute value of x-y < 1/3 in the square formed by (0, 1) of X and (0,1) of Y.

The area of this area/1 is the probability of 5/9.