I think because it was altready after 6:00AM as he was investigating the murder scene and the alarm was in a noted "set" mode.
Whatever style of alarm, we are to understand that if it was for 6:00AM and had gone off already, the setting/button/switch/indicator would be in an "off" type position.
Not only that, (what Bob said), but recall that Columbo checked Harold's shoes and (RIPE) socks. He was commenting on how much his own feet sweat, and that was more proof that Harold had very recently taken off his shoes/socks. Oh, and the bed didn't look to be "slept in" either.