Note that when the trillion were told they won, they were actually being lied to - they had won a trillionth part of the prize, one way or another.

Suppose that, instead of winning the lottery, you want your friend to win the lottery. (Or you want your random number generator to crack someone's encryption key, or you want a meteor to fall on your hated enemy, etc.) Then each of the trillion people would experience the full satisfaction from whatever random result happened.