I began using a skeleton spawner for exp and I used a trident killer created by a youtuber named silentwisperer(see link below). I was playing on hard mode. Although the skeletons, when killed using a normal item, such as a sword, axe or a thrown trident, dropped their armor and bow at a normal rate, they did not drop anything when the trident killer was used. This has also happened with zombie farms. I have also consulted with some of my friends who report having the same problem on Windows 10 edition too.

Silentwisperer's trident killer: https://www.youtube.com/watch?v=lUC9N-vg7Ys