1. no possibility of doing or achieving something
you haven't a hope in hell of getting that promotion
This is a very casual informal phrase meaning there is no chance of something happening. It is related to the expression 'not a snowballs hope in hell'. Hell is considered to be full of fire and heat so the snowball would have no chance of surviving. When you say there 'isn't a hope in hell' of something happening you mean there is absolutely no possibility it can happen or be achieved.