I may misunderstand you, but replace the lottery with a coin toss. Buying a ticket gets you a 50% chance of winning. This reduces the pool of possible outcomes

I may misunderstand you, but replace the lottery with a coin toss. Buying a ticket gets you a 50% chance of winning. This reduces the pool of possible outcomes by 1 for the next choice, so there is precisely one choice left. However buying a second (different) ticket does not give you a 150% chance of winning.