And the odds are even worse than your estimates- I counted 29 winners of 5+ games in the past five seasons, so even then, your estimate is almost cut in half. making the probability substantially lower.
Sorry, I somehow read your post as 'three seasons' instead of five.
I have a real problem with a blind statistical analysis of something that is so performance-based. Certain people do better in this game than other people do, and that is not something you can calculate. Even starting with the idea that three players have an equal chance to win gets you off on the wrong foot as far as I'm concerned.
I wasn't really intending that to be scientifically accurate; I was trying to justify why we have only seen one ten-game winner in the last eight years since I would have guessed we'd have more.