This took place in a Burger King parking lot, in front of a couple of dozen people, after Davis and his buddy had attracted everybody's attention by pistol-whipping a homeless man who was screaming for help. The eyewitnesses did not know each other, but all of them independently described to a 't' Davis's clothing and appearance, and picked him out of a lineup. A couple of them knew him by name. When you get consistent, independent statements, that's a pretty good indication of truthfulness. See Susanna and the Elders (Daniel ch. 13).
Forensic evidence: Davis just a short time before shot somebody at a party. The shells recovered from that shooting scene matched the shells recovered from the shooting of the police officer. The pistol was never found because Davis threw it away (and told a friend he threw it away).
More forensic evidence: police found the officer's DNA on Davis's bloody clothing, which he had discarded at his mother's house. That evidence was not introduced at trial because his mama lied after the fact and said she had not given permission to search the house. But there it is.
Additional evidence: Davis admitted to two friends that he had shot the police officer because he got a good look at his face and could identify him. That doesn't include the jailhouse rat who retracted his not-very-believable statement (the details didn't match up with any of the eyewitness accounts).
Finally, the officer identified Davis over the radio before he was murdered. Identification from beyond the grave good enough for you?
I had been trying to find if the guy had a record, but couldn't find any stories about that.