cannot be (impossible)
Expresses strong logical impossibility, 'there is no way that...'
This pattern conveys that based on evidence or logic, something cannot possibly be true. It's stronger than just saying 'probably not'—it's more like 'there's no way.' For example, if someone says he studies all day, you might say あの人が勉強をしないはずがない 'There's no way he doesn't study.'
Use it when you are certain that a situation is impossible because of known facts. It is common in both speech and writing, but in casual conversation you might hear はずない (without が). However, the full form is perfectly natural.
Note that はず comes from the noun meaning 'expectation' or 'reason', so はずがない literally means 'there is no reason/expectation that...'.