, 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'.
(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.
Because I left the house an hour early, it is improbable that I will be late. (That I am bound to be late is not true)
It is hardly possible that this box is heavy. (It is not the case that this box is bound to be heavy)
It is highly unlikely that Sally's house is splendid. (That Sally's house is sure to be splendid is not the case)
It is highly unlikely that the person over there is Tom.
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.
His car would not be expensive. (His car is bound to not be that expensive)
It is hardly possible that his car is expensive. (That his car is bound to be expensive is not true)