Have you ever heard the Biblical quotation about how a rich man’s chances of getting to heaven are about the same as a camel passing through the eye of a needle?
An eye is an ancient reference to an opening in a wall or a gate, because you could see through it.
If there is an obstruction, or in the case of the alley, a wall, then there is no “eye” to see or escape through, it is a blind alley.