The probability of an event not happening is equal to (1 - the probability of the event happening). In this case, if you have a 1/20 chance of hitting the event, then the probability of not hitting it is 1 - 1/20 = 19/20.
In North American racing, the three most common ways to bet money are to win, to place, and to show. A bet to win, sometimes called a "straight" bet, means staking money on the horse, and if it comes in first place, the bet is a winner. In a bet to place, you are betting on your horse to finish either first or second.