I've been running a zombie farm for the last few days that converts zombies into drowned, and thus gives access to drowned drops. No matter how many are killed, no trident drops occur. The same applies to drowned that have naturally spawned in, with and without tridents. I have killed exactly 580 drowned, and still no luck. I've begun to think that luck has no bearing on this, but rather a bug has interfered with this.
and I've been using a looting 3 sword the whole time.