Exculpation is the noun that sits on the verb exculpate: the act of proving someone is not guilty, or the cleared state you reach after that proving. You might read of “his exculpation” after a trial, meaning people now accept he was not at fault. Same formal, legal flavour — news about courts, academic writing, almost never ordinary speech. Though actually, writers sometimes stretch it toward “a story that gets someone off,” which can sound a little like making excuses. In careful use it still means the blame was shown to be wrong, not merely talked away.