If the chance of anyone winning is y and the prize is x, you can pay the insurer (x*y)+z dollars to pay out the x dollars in the event that someone wins. I'm sure z is probably tied to x in some way, but just know that z is the money that turns into the insurer's revenue in the long run.

You're basically paying the expected value(cost?) of the prize, plus a fee to the person who's insuring you. That way a billion dollar contest will not actually cost you a billion dollars, even in the event that someone wins.

"I'll pay you $1 million now. If anybody wins the prize, you're on the hook to give them the other $999 million. If nobody wins the prize, you get to keep the $1 million."

edit: And where I say $1 million, do some hand waving with the odds and figure out a number on which both parties agree

Buffet is the one (via one of Berkshire Hathaway's insurance companies) who is doing the insuring. Quicken loan is paying buffet/berkshire a, likely large, premium to pay the billion if someone wins. Given the odds are 1 in not gonna happen, it's likely an easy million or two for buffet, and free promotion. Buffet/Berkshire also insured the pepsi billion dollar prize thing a few years back.