For four seasons, Viola Davis has starred for ABC in “How to Get Away With Murder.” Her new series for the network, “The Last Defense,” might well be called “How to Get Convicted of Murder.”

The seven-part documentary, starting Tuesday, reargues cases of two prisoners awaiting execution. It begins with Ms. Davis (one of several executive producers) saying in a voice-over that every year an average of five prisoners on death row are exonerated.

“The Last Defense” may or may not add to that number. But it offers a powerful argument that people can be convicted as much by emotion and prejudice as by evidence.

The first four episodes re-examine the 1997 murder conviction of Darlie Routier, a Texas woman whose two young sons were stabbed to death.