From the Super Mario Wiki
Mario Kart DS
Triple Bananas first appear in Mario Kart DS. When used, three Bananas are deployed to trail behind the player's kart. The player may throw each Banana one-by-one whenever they please, and can also use the Bananas to block incoming items. Triple Bananas appear only in the top three positions in Grand Prix and VS modes, usually with slightly smaller probabilities than Fake Item Boxes; in Battle Mode, they are usable only by human players, and usually appear when the player ranks near the middle.
Mario Kart Wii
Triple Bananas return in Mario Kart Wii, behaving exactly the same as in Mario Kart DS. They appear only in the top four positions for human players and top three for CPUs in Grand Prix and VS modes; Battle Mode probabilities are stable for CPUs, but do not appear for poorly-performing human players.
Mario Kart 7
Triple Bananas return in Mario Kart 7, behaving exactly the same as in past games. In Grand Prix and VS modes, they can usually only be obtained in the top two positions; in Battle Mode, human players can only obtain Triple Bananas at or near first place, though CPUs have a fixed probability in obtaining them.
Mario Kart 8 / Mario Kart 8 Deluxe
Triple Bananas return in Mario Kart 8 and Mario Kart 8 Deluxe. This time, when deployed, the Bananas orbit the player's kart rather than trailing behind it, though everything else functions the same. In Grand Prix and VS modes, all players may obtain Triple Bananas 1000-2000 units from the frontrunner; in Battle Mode, they can only be obtained when the player has only one balloon left one minute into the game.
Mario Kart 7
Mario Kart 8