The information should be readily available online but here’s an oversimplified explanation of how I believe the lottery works. The PowerBall (and MegaMillions) is a multi-state game so there are more people playing than a typical lottery.
Let’s say a ticket is $2, for each ticket sold the jackpot increases by $2 but only 65% of the ticket sale needs to go to the jackpot (since it’s annuitized over 20 payments or a lump sum of much less is paid out). 10% or so goes to the retailer, I’m not sure how much is set aside for smaller prizes (although the expected value could be easily calculated) and the rest goes to the gaming commission which distributes the bulk of it to stuff that taxes would otherwise pay for.
Let’s say someone just one the lottery and cleared out the jackpot. Actuaries will estimate that say 10,000,000 million tickets will be sold, therefore they’ll estimate the jackpot at $20,000,000. With roughly 300,000,000 possible outcomes and 10,000,000 tickets sold- the odds of a winner are 1/30.
If no one wins there’s already $20,000,000 in the jackpot. Actuaries will estimate that they can raise the estimated jackpot to $45,000,000 since at that size 12,500,000 tickets will be sold. With each subsequent drawing that no one wins the jackpot goes higher and even more tickets are sold.
The past drawing was for an estimated $1,000,000,000 and no one won. If the next estimated jackpot is $1,200,000,000 that means that 100,000,000 tickets are estimated to be sold and the chances of a winner are 1/3.
The previous drawing was on a Monday and the next one is on a Wednesday. Had the previous drawing been on a Wednesday with the next one on a Motzaei Shabbos the estimate jackpot would have been much higher. Actuaries took into account that the time between the two drawings is two business days and no weekends or legal holidays.