unbelievably

(manner) In a manner that one does not believe.

“He gestured unbelievably. Everyone knew he was faking being sick.”

(degree) To an extent not to be believed.

“His face turned unbelievably blue. We realized he was actually choking.”

(evaluative) Contrary to expectations, amazingly.

“Unbelievably, Rudy saved the man's life but got sued for breaking two of his ribs.”