Let x be the distance of AC and y be the distance of BD, which satisfies x+y.

And the distance is not less than 40, that is, x≥40 and y≥40. Seen from the diagram, it is a triangle surrounded by straight lines x=40, y=40 and x+y= 120.

So the probability is the area of a small triangle divided by the area of a big triangle, both of which are isosceles right triangles. The waist of a small triangle can be calculated as 40, so the area is 40*40/2=800, and the waist of a big triangle is 120, so the area is 120* 120/2=7200, so the probability is 65400.