筈(はず)がないHardly possible, Cannot be, Highly unlikely, Improbable

Like はず, coming from the kanji 筈(はず), which suggests that something is 'bound' to be true, はずがない suggests that something is 'not bound' to be true. This expression is usually translated as 'hardly possible', 'improbable', or 'unlikely', but in reality, it is a bit weaker than these, and translates more literally to '(A) is not the only possibility'.

As はずがない (a combination of 筈(はず), the case-marking particle が, and the い-Adjective ない) is a phrase that starts with a noun, it may be used after any word that could usually connect with a noun.

Caution

There is a big difference in nuance between ないはずだ 'bound not to', and はずがない 'not bound to'. ないはず strongly negates the (A) statement, and expresses the speaker's opinion that it is almost definitely not true. はずがない on the other hand, simply suggests that (A) being almost 100% true is not the case.