When a Skeleton kills another mob that was attacking it†, the Skeleton will shoot arrows indefinitely into empty space, in the direction of where its opponent was before it died. Note that if the Skeleton sees the player it will come to its senses and attack the player.

What I expected to happen was...:
After the Skeleton kills its opponent, I expect it to return to random roaming or (BONUS BUGFIX GOAL!) pathfinding to the player if it was doing so before the other mob attacked it.

What actually happened was...:
The Skeleton stands still and shoots at nothing until he sees a Survival mode player or has to hide from sunlight or something.

Steps to reproduce:
1. Stand near a Skeleton with a Spider/Blaze/Skeleton in between the Skeleton and the player.
2. Let the Skeleton shoot his arrow and hit the Spider/Blaze/Skeleton, initiating a fight between the two mobs.
3. Upon killing the other mob, the Skeleton will continue to shoot at the location where the other mob was when it died.

Notes:

• If you nudge a Skeleton shooting at nothing in Creative mode (so that he doesn't see you) and move him to a different location, he will still aim at the spot where his opponent died.
• This behaviour does not exist with Blazes.
• Depending on how far away the Skeleton is from where his opponent died, he will vary his rate of fire, like he's supposed to with living mobs. It even changes if you push him farther or closer to the spot where his opponent died.

†For example, if it accidentally shot a Spider/Blaze/Skeleton, and the Spider/Blaze/Skeleton attacked it and they got in a fight. This therefore won't work with a Zombie because Zombies don't attack Skeletons (see my other bug post).