the wiki (https://minecraft.gamepedia.com/Trident) says this: "Drowned can also drop a trident as one of its normal drops. The trident has a 11% chance, 13% chance with Looting I, 15% chance with Looting II, and 17% chance with Looting III of dropping itself."

I have been killing drowneds using a looting 3 sword for a while now. and while trying to obtain a trident, I've got 25 gold ingots. since the chances of getting a gold ingot are 7% when killing a drowned with looting 3, the amount I had to kill in order to get these 25 gold ingots is approximately, 357 drowneds.

the chances of getting a trident (according to the wiki) is 17%. that means the chances of not getting a trident after killing 357 drowneds are 0.0000000000000000000000000013%