Because the people who are consistently right will consistently win money and will make bigger bets which move the price more, in the limit case making the price converge on the true probability of the outcome.
This is the theoretical underpinning of prediction markets.
Equating being "consistently right" with having a sufficiently large stash of capital is ludicrous.
"right" people will wisely take most their winnings out of a high-variance market. "wrong" people with deep pockets (or lots of wrong people with shallow pockets) will continue to distort the market.
they can only do so as long as they have enough capital to lose. Because every time they try to move the betting markets against the truth, they will simply lose that money when the event happens (and turns out they were wrong).
So any distortion will merely be temporary. Unless they have access to unlimited capital of course - which is not true yet for anyone (but the US gov't).
Apart from minor effects, the price is the probability. If you 'know your shit', you have more confidence and thus bid up or down until there are no more counterparties willing to accept your price, and thus the price settles at approximately the expert/insider probability.
like any signal, you reflect on it, integrate it into your belief, think through the consequences, etc.
we all want mr. delphi to tell us exactly what will happen. but without such a friend, we reason under uncertainty. markets are one tool we've found to coordinate such signals.
would you ask the same of hiring a private investigator, or paying for the new york times? there is no authority with your interests but yourself; you must choose who to trust.
This is the theoretical underpinning of prediction markets.