Minecraft wiki entry for Acquiring_a_conduit, associated text: Bedrock Edition: Drowned have an 8% chance to spawn holding a nautilus shell. If it is holding a nautilus shell in the offhand it is a guaranteed drop. Also, converting zombies into drowned resets the drop counters, giving newly-converted drowned the same chance to spawn with a nautilus shell. Therefore, nautilus shells are most easily obtained conduit ingredient in Bedrock Edition. If you find a dungeon with a zombie spawner, then building a basic flooded dungeon drowned farm is the simplest and most efficient way to produce nautilus shells in Bedrock Edition survival mode, yielding more nautilus shells than a player would ever need.
Java Edition: Drowned have a 3% chance to spawn carrying a nautilus shell. If they do, they are guaranteed to drop it. Only naturally-spawned drowned carry nautilus shells; zombies converted to drowned do not.