I didn't quite understand how Poirot found out Ratchett was indeed Cassetti. I guess it was based on the burned note found in his room, but the note was so vague, how could he be so sure?
Also, why was the note burnt and left there?
I hope some good soul can enlighten me :)
Thanks!
The note was burned because it was evidence and they were trying to destroy it. It was left there because they apparently thought it had been sufficiently destroyed.
When Poirot was able to reassemble the note, he was able to fill in the missing letters simply because he is so clever. And once he had the original note intact, he was able to deduce that Ratchett was Cassetti.
I was a bit confused by this as well, the first time I saw the movie, because it wasn't clear to me that the police in charge of investigating the original crime had figured out Cassetti was the culprit. But there's a line later in the film that indicates this is so. So apparently Cassetti is on the run and living under the name of Ratchett.