Minecraft wiki entry for Skeleton, associated text: 0–2 bones. The maximum drop is increased by 1 per level of Looting, for a maximum of 0-5 bones with Looting III.
0–2 arrows. The maximum drop is increased by 1 per level of Looting, for a maximum of 0-5 arrows with Looting III.
Picked-up items have a 100% chance of dropping and drop with the same damage level it had when picked up.‌[Java Edition only]
Any naturally spawned equipment (including the bow) has an 8.5% chance of dropping if killed by the player (9.5% with Looting I, 10.5% with Looting II, and 11.5% with Looting III). It is damaged and sometimes enchanted.
A skeleton drops its skull if killed by a charged creeper's explosion.
Skeletons drop 5 when killed by a player or tamed wolf and extra 1–3 if the skeleton has equipment.