I think this is what you are looking for:
https://88probett.com/horse-race-betting-101-understanding-how-to-read-horse-racing-odds/
The important part is that the betting odds are not the same as the actual odds of winning. It just reflects where people are placing their bets, so that the house can entice more bettors, but still have their risk evenly spread so they'll make a profit no matter who wins.
So does that mean the first person to place the bet is looking at 0:0 odds?
No, they have starting odds, and change as needed. Or most local bookies just follow Vegas odds.
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