not have a snowball's chance in hell
not have a (snowball's) chance in hell
To be completely impossible or incredibly unlikely; to have no chance whatsoever. Usually followed by "of." That party doesn't have a snowball's chance in hell of winning an election in this part of the state. We don't have a chance in hell of catching up to their score.
not have a ˌsnowball’s chance in ˈhell (of doing something)(informal) have no chance at all of doing something: Look at this traffic! I’m afraid we haven’t got a snowball’s chance in hell of getting to the airport in time. OPPOSITE: a sporting chance
This idiom refers to the belief that hell is a place of fire.