And here we are 14 years later (2019) and i was wondering the same thing. Tried to 'shazam' it, but shazam couldn't identify it. Searched w/google, & found *your* query & subseqent answers. I can confirm that that version is very much like the Cowboy Junkies' version... who i hope you've subsequently discovered & liked.
No, Cowboy Junkies version is much closer.......but even the Cowboy Junkies version is not as good as the version that is in the two episodes of Columbo. I am assuming that both versions (in the two Columbo episodes) are the same.