Great question.

As I recall, Patrick and Columbo were already at Barney's and THEN Mrs. Calvert walked in, having been given a ride by the officer who spends most of his time looking for the key witness - THE CAT. If she came with the officer, then how did Columbo and Patrick get there? And why did they go back to police headquarters in the same car? Were they get dropped off by someone else? Did they take a cab, like Alvin Deschler or Verity Chandler? Columbo would have a field day with the these "loose ends" which don't make sense.

P.S. - funniest thing happened when I had to VERIFY this post - the pictures came up and I had to identify the TAXIS!!!

No, he did not ride with them on the way to the restaurant. At Barney’s he asks Mrs. Calvert if the officer who drove her over had any trouble finding the place. Also, if Columbo rode to the restaurant with them, he would’ve known where she sat, and wouldn’t have needed to ask the officer in the garage where she sat. How Columbo and or Patrick got to the restaurant is not known. It seems that maybe Columbo got into the car because he was feeling sick. Patrick’s transportation on the way over is also not disclosed, and the complete scene (from the beginning of the restaurant to the end of the parking garage) also indicates that he did not ride Mrs. Calvert on the way over.

Columbo and Pat were already at the restaurant. I'm sure that Columbo had already inhaled a whole bowl of chili.

Columbo gets very lucky in this one because if the wedding photographer did not take a picture of Clifford and Kathleen dancing the whole case goes up in smoke.

As Columbo says in "Columbo Goes to College", "And luck. You have to be lucky."

He's always lucky.