According to Life: the Odds (and How to Improve Them) by Gregory Baer, the odds of a hole in one on a par 3 hole in the PGA tour is 1 in 2491. I believe those distances fall in the par 3 range.
A 1 handicap is darn good, so I'm not going to give much of a discount compared to PGA Tour players. Let's say your son's probability per par 3 hole is 1 in 3,000. A typical gold course will have about four par 3 holes. Let’s say your son plays every day. That would be 28 par 3 holes a week. The probability of making exactly two hole in ones would be combin(28,2)×(1/3000)2×(2999/3000)26 = 1 in 24,017.