Call Northside 777 (1948), directed by Henry Hathaway.
Slow, methodical tale based on a true story: a reporter becomes convinced that a man jailed for 11 years for killing a policeman is innocent. Realistic look and earnest tone, and said to be one of the first films made on location in Chicago. Documentary-style narration at the beginning, vanishing until once in the middle and end.
Jimmy Stewart is the reporter, Lee J. Cobb his editor. Richard Conte, almost always a thug in his career, is here the innocent prisoner.
Stewart is a cynical man, although he has a warm home life. He only slowly comes to believe in the prisoner. In a more fictionalized account he would have a running and shooting encounter with the real killers, but that doesn't happen here; we never even find out who they are.
It's pretty low-intensity drama. A key bit of evidence is a photograph zoomed to an impossible level of detail, a screen-writing trick still used today.