Shama-il Tirmidhi Chapter 023, Hadith Number 001 (130).

Kaa'b bin Maalik Radiyallahu 'Anhu says: "Rasulullah Sallallabu 'Alayhi Wasallam licked his fingers thrice (after eating)".

Commentary.
After eating it is mustahab to lick the fingers before washing the hands. According to some authorities, due to this narration it is mustahab to lick the fingers thrice. Mulla 'Ali Qaari says three times is not meant here, but that three-fingers should be licked, as will be stated in another narration. Therefore, another narration of Sayyidina Kaa'b bin Maalik Radiyallahu 'Anhu is also mentioned in this chapter. Some commentators of the hadith say that it is a separate etiquette to lick the fingers thrice, so that it becomes completely clean, and in another narration where three fingers are mentioned, is also one of the etiquettes.