I've converted many zombies into drowns and hunted them out in oceans, but none have ever dropped a single trident even after killing hundreds of them. I went into creative for a bit and used drowned spawn egg and those spawned with tridents and dropped them, but not naturally occurring ones or converted ones have ever.
MC-134435
Drowned not spawning with or dropping tridents
Resolved
Duplicate
0
Only non-zombie-converted-drowned have a chance to spawn weilding a trident, this chance is about as low as a zombie spawning holding a sword or shovel; and only when they weild a trident, they have a small chance to drop it (same chances as getting other naturally spawned mob equipment).
You’ve just been unlucky.