To be clear, I'm not suggesting that playing the lottery is a rational thing to do, because it isn't.
However whilst each ticket has the same chance of winning, more tickets = more chances. Taken to extremes, the overall chance of winning would be very high, for example, if you were to buy 20 million tickets.
Edit: apparently it's around 45,000,000:1 for the jackpot so my example should be more like 50 million tickets. Same principle though.