First past the post is a popular term you will need to be aware of in horse racing betting. This is simply the name of a promotion that is set by the bookmakers where they payout on the horse which finishes first, regardless of what happens to that horse.
For example, if there is a situation where the horse crosses the line first but is then demoted to second as the horse interfered with the other following a stewards’ enquiry, with the horse which finished second being awarded the winner, the bookmakers will still have to pay out on the official winner, which is where the ‘first past the post’ comes into play.