give the benefit of the doubt
give the benefit of the doubt {v. phr.}
To believe (a person) is innocent rather than guilty when you are not sure.
The money was stolen and John was the only boy who had known where it was, but the teacher gave him the benefit of the doubt.
George's grade was higher than usual and he might have cheated, but his teacher gave him the benefit of the doubt.
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Source: A Dictionary of American Idioms