The ITB betting mechanism appears to have a mechanism to determine the probability of the player winning.
RNG mechanism[]
According to my tests, it appears that the initial probability of a horse winning is around 1/5 (20%). When the player places money beyond $10,000 the game will then drop the probability to around 1/25 (4%), making it significantly harder to win. This of course can be mitigated by saving prior to betting, loading the save if they lose, or saving the game if they win.
Odds displayed doesn't affect the probability at all. Always pick the teal horse (with 11/1 or 12/1 odds) to get the most money as you'll get 12 or 13 times more cash than when you begin with if you win.