Folks,
Because they're awarding the prize to every hole-in-one in the single-play tournament, they are simply offering 1,000:1 odds against each player making a hole-in-one. Anyone who has played this game for a while has probably holed an occasional long approach shot, but you can imagine how often that happens for you at your own skill level.
Each player is making an independent (side) bet against the house, unrelated to the behavior of any other players.
WGT knows exactly what the odds are across all players. If they are limiting entries to 10,000 players, I assume the real odds are greater than 1,000:1 but considerably less than 10,000:1. This is because they probably do want to have at least one winner. It just looks better that way.