Mr. Gatling’s exoneration will be the 20th time in the last two years that the Conviction Review Unit has helped to clear defendants found guilty in Brooklyn of crimes they did not commit. Charles J. Hynes began a similar effort as the district attorney in 2011, but when his successor, Ken Thompson took office in 2014, he renamed the unit and put his support squarely behind it. The review unit initially focused on cases connected to one detective, Louis Scarcella, whose alleged misconduct has called into question nearly 50 murder cases. But as news of the unit’s work has spread, its reach has widened to include cases like Mr. Gatling’s.

Mr. Gatling’s ordeal began on Oct. 15, 1963, when a man armed with a shotgun burst into the home of Lawrence Rothbort, an artist who lived on Bedford Avenue with his wife, Marlene, and their two children, a 6-year-old boy and an infant daughter. According to police reports and, later, testimony at trial, the man demanded money from Mr. Rothbort. When the artist refused, the gunman shot him in the chest.

During the investigation, suspicion first fell on Mr. Gatling when one of the Rothborts’ neighbors, a felon named Grady Reaves, informed the police that he had seen Mr. Gatling in the area just minutes after the shooting. When Mr. Gatling was interviewed by detectives in the 80th Precinct (which was later absorbed by another precinct), he told them that he had been paying his rent at the time — a fact that his landlord eventually confirmed. A few hours into the interview, Mr. Gatling’s lawyer called the station house, but the detectives told him that he could not see his client until the questioning was complete, court papers say.

Image Mr. Gatling in a portrait taken while he was in prison.

That same evening, Mr. Gatling, who was 6-foot-1, was placed in a lineup with three notably shorter men. Mrs. Rothbort was called in to identify him, but did not pick him out, even though, court papers say, the detectives directed her to focus on “the tall one.”