Use 'improbability' to express skepticism or doubt about an event occurring. Given the improbability of winning the lottery, I don't bother buying tickets.
Pro Tip 2/3
Not Impossible
'Improbability' suggests something is very unlikely, but not completely impossible. The improbability of getting a perfect score shouldn't discourage you from trying.
Pro Tip 3/3
Nuanced Expectation
It subtly conveys that while an event is unexpected, its occurrence would be acknowledged. He smirked at the improbability of the quiet student answering the question, yet she did.