Whatever the history is, the book's very short, 116 pages in the edition I have, which I bought back in 1963 or so. The narration is a lot like a film voiceover, and you can see it playing out as the Scotland Yard man, Calloway, tells his part and then fades into the third person for the story itself.
Rollo Martins shows up in post-WWII Vienna to see his old school friend, Harry Lime, only to discover that Lime has died in an auto accident. There are a couple of witnesses on the scene who load him into an ambulance, and a third man sees the events from a window above. His story is different from the one the others tell, and indeed he mentions another third man, one at the scene of the accident. Martins is determined to find out the truth, and pretty soon people start to die.
The movie was such a big success that it spun off a radio prequel, The Lives of Harry Lime, with Orson Welles playing Lime as he did in the film. The idea was that Lime, who was quite the villain in the movie, wasn't so bad earlier in his life, more of a hapless conman than someone with the heartless, cynical view that he later developed. In the intro to the show (I've heard a few episodes on XM), Welles gives away the ending of the movie.
Later on there was a TV series, The Third Man, with Michael Rennie playing a thoroughly rehabilitated Lime. He's more or less a legit businessman, far more sympathetic than the character in the book and movie.
But back to the book. Would The Third Man be published today? Up until the end of the novel, almost all the action is off-stage. The narration is odd, as I've said. The first two paragraphs take up more than two pages, so it's obviously not in the current thriller style. Lots more emphasis on character and setting than action, though the final chase through sewers is a good one. In the end, though, I really don't think this one would be much to the taste of anybody over thirty. As for old-guy me, I had fun re-reading it.