2019 AIME I Problem 2

Jenn randomly chooses a number J from 1, 2, 3,\ldots, 19, 20. Bela then randomly chooses a number B from 1, 2, 3,\ldots, 19, 20 distinct from J. The value of B - J is at least 2 with a probability that can be expressed in the form \tfrac{m}{n}, where m and n are relatively prime positive integers. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.