To the best of my knowledge, there should be an 8.5% chance of a weapon drop every time I kill a monster equipped with one. However, I have not once collected an iron sword or shovel from a zombie, a golden sword from a zombie pigman, a bow from a skeleton, or a stone sword from a wither skeleton throughout all of my playing MCPE (which includes running tests on hundreds of skeletons).
I would very much appreciate if this bug is fixed, it's one of those little features that make MCPE so enjoyable!
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In which difficulty are you playing?

Maximum difficulty, as always! My mobs will graciously give me way too much armor (MCPE-9846) but they are very stingy in the weapons department.

Other than Skeletons, no mobs in PE have ever dropped weapons besides skeletons. From my experience, I haven't seen a skeleton drop a bow in many versions. We'll keep this bug open primarily because of the skeletons issue since other mobs dropping weapons is technically a feature request.

This is still an issue. I just built a skeleton XP farm based upon a spawner I found. I get tons of arrows, bones, and armor. I just haven't gotten even one bow from the hundreds of skeletons that have died in the farm so far.
Confirmed on version 0.15.4 - Windows 10 Edition
If you need a world download I will gladly provide one.

Please respond and add the current version if you can reproduce this issue.

Windows 10 Edition - 0.15.4
I can't attach my world download as it exceeds the 10 MB limit in Jira. Here is a link to the world map that I have up for download:
https://drive.google.com/file/d/0B2G-ONKmAfUlMC12WHR0dVJHdkU/view?usp=sharing
There is a stairwell just behind the house that leads down to the skeleton spawner. Turn on the lever on the wall to put it into XP mode and you can kill the skeletons yourself and see that they will never drop a bow only bones, arrows, and way too much armor.

I can confirm this in 0.15.4. I have killed hundreds of skeletons so far but I haven't got any bows from them.

This issue relates to MCPE-10384

zombie pigman don't drop enchanted swords.

Fixed in version 0.16.0 build 1
You are right. According to the Minecraft Wiki: Mob Drops (Equipped Items), there should be an 8.5% chance of dropping them. I have never experienced this happening on MCPE.