expression, noun-modifying (irregular)
that is not supposed to ...; that ought not to ...; that should never ...; that cannot possibly ...
Prenominal phrase expressing strong denial of expectation or possibility; used to modify a noun and convey that something is unthinkable or contrary to what is expected. Often interchangeable with はずがない, but はずのない directly modifies a noun.
See also: はずがない
He is a person who would never do such a thing.
It's something that couldn't possibly be unsolvable—such a simple problem.