The thinking isnt that that you putting money on a horse to win increases it’s odds of winning, its that by signalling your belief that you think it will happen by a costly signal (you lose the money if you are wrong) you are updating the overall odds to be closer to the true probability by the power of crowds. if 200 people are betting something will happen and only 10 are betting it wont then that is evidences that the thing is more likely than not to happen.

There are flaws in this thinking, it doesnt take into account manipulation of events to win bets is a particularly big one, and it also gets worse the more removed the thing being bet on is from everyday life as people make less informed choices.