Take that letter and check to the police immediately. If you didn't buy a ticket, you haven't won anything -- this is a lottery and fake check scam. If you try to deposit that at the bank, you can get in serious trouble -- depositing subject to collection will protect you financially and legally, but there's 0% chance it's a good check so why bother?
To quote from fraud.org --
"The checks are fake but they look real. In fact, they look so real that even bank tellers may be fooled. Some are phony cashiers checks, others look like they’re from legitimate business accounts. The companies whose names appear may be real, but someone has dummied up the checks without their knowledge.
You don’t have to wait long to use the money, but that doesn’t mean the check is good. Under federal law, banks have to make the funds you deposit available quickly – usually within one to five days... But just because you can withdraw the money doesn’t mean the check is good, even if it’s a cashier’s check. It can take weeks for the forgery to be discovered and the check to bounce.
You are responsible for the checks you deposit. That’s because you’re in the best position to determine the risk – you’re the one dealing directly with the person who is arranging for the check to be sent to you. When a check bounces, the bank deducts the amount that was originally credited to your account.... In some cases, law enforcement authorities could bring charges against the victims..."