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.

• 1時間（じかん）も早（はや）くに家（いえ）を出（で）たから遅（おく）れるはずがない。
  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)
• この箱（はこ）は重（おも）いはずがない。
  It is hardly possible that this box is heavy. (It is not the case that this box is bound to be heavy)
• サリーの家（いえ）は立派（りっぱ）なはずがない。
  It is highly unlikely that Sally's house is splendid. (That Sally's house is sure to be splendid is not the case)
• あそこにいる人（ひと）はトムのはずがない。
  It is highly unlikely that the person over there is Tom.