"Okay, let's hear it, Columbo."
Secretary of State Elizabeth McCord
Tea Leoni's political thriller TV series has to take place in an alternate TV dimension since their President is different from the POTUS to be found in Earth Prime-Time and the Trueniverse. (Because of the possibility of jokes at the President's expense, the President in Toobworld should always be the same person as in the real world.)
Many characters (and situations) in the dimension of 'Madam Secretary' are different from those to be found in the main Toobworld, but that doesn't mean none of the other characters from other TV shows can't be found in Liz McCord's world. And Lt. Columbo would be a good example.
However, he doesn't have to be the rumpled detective that we knew and loved as played by the late Peter Falk. This could be the very world in which we would find the original TV Columbo.....
I've mentioned the "Enough Rope" episode seen on 'The Chevy Mystery Show' before. In 1960, the genius writing team of Levinson & Link created the character who was brought to life by Bert Freed. It was the same story as seen in the later Broadway-bound stage show which starred Thomas MItchell (who unfortunately died in the touring production.) The title was changed to "Prescription Murder" which was adapted yet again for TV to serve as the first pilot for the eventual 'Columbo' series.
Usually the Toobworld Dynamic rule was to have the first performance of a character to be the official one for Toobworld. But there are exceptions and this is one of them. There were far too many episodes of 'Columbo' with Peter Falk to not consider him to be the Columbo of Earth Prime-Time.
And that means Bert Freed must be shuffled off to another world. Normally, they would go to Prequel Toobworld, along with certain TV pilots (because of recasting usually) or productions in other anthology shows. (A good example of this is Horace Ford, first played by Art Carney in 'Studio One' and then by Pat Hingle in 'The Twilight Zone'. Both versions of "The Incredible World Of Horace Ford" were one-shots, but it's the latter episode which has shown to have a longer shelf-life in syndication and on DVD.
But in this case, why not send Bert Freed's Lieutenant to the world of 'Madam Secretary'? Since Liz McCord mentioned him by name, that doesn't have to mean she was referring to the TV show. The Columbo of her world could have been just as famous as the one in Toobworld - he could have solved headline-grabbing murders like those committed by world-famous authors, painters, photographers, symphony conductors, football team owners, senatorial candidates, and even a Suarian ambassador.
So even in an alternate Toobworld, Lt. Columbo was real. He just didn't look like Peter Falk. But Falk played the detective not only in the main Toobworld, but also in Skitlandia - as seen the 'Dean Martin Roast' of Frank Sinatra and in an 'Alias' crossover sketch seen during the ABC anniversary special.