Precisely. You absolutely do have a chance of winning any honest lottery. And yes, it's microscopically small but it's greater than 0.
For a time the Washington State lottery was constructed such that you had a one in 7 million chance of winning. Every time the jackpot got over 7 million - and that was fairly often - that one-dollar ticket was actually a valid bet. Your chances weren't any better but the reward was more than commensurate with the investment.
They changed it when it became obvious that was a losing proposition for the state. Mind you, they actually could have run it indefinitely at a loss as long as the interest they made on the principal was greater than the loss. But that sort of obviates the lottery as a method of funding.
It's entertainment. If the emotional lift and the amusement you get when you purchase a ticket at astronomical odds is worth the buck, then by all means play. For me it isn't, and I don't.