In a​ lottery, the top cash prize was ​$646 ​million, going to three lucky winners. Players pick five different numbers from 1 to 54 and one number from 1 to 49.

A player wins a minimum award of $525 by correctly matching three numbers drawn from the white balls​ (1 through 54​) and matching the number on the gold ball​ (1 through 49​). What is the probability of winning the minimum​ award?