Here are some synonyms for improbable:
* Unlikely
* Unfeasible
* Unrealistic
* Remote
* Doubtful
* Slim chance
Examples:
* It's improbable that I'll win the lottery. (There's a very small chance, but it's not impossible.)
* The team's victory was improbable after being down by so many points. (It was unlikely they would win.)
* The scientist's theory is improbable, but it's worth investigating further. (It's unlikely to be true, but it's not impossible.)
The opposite of improbable is probable or likely.