I was making a bunch of command block things, because that's what I'm in to lately, when I tried making a Leprechaun. I spawned it in and noticed it wasn't dropping its carrot on a stick. So, I then set it to 100% drop chance. Still no drop. After, I attempted a few more times, just the plain zombie drops. So, I tried a mob that previously dropped items, and the same thing happened. Then I tried another world, same thing.
How to Reproduce Issue
1) Give yourself a command block (/give @p command_block)
2) Paste in this command /summon zombie ~ ~1 ~ {HandItems:[{id:diamond_sword,Count:1b},{}],HandDropChances:[1.0F,1.0F]}
4) Kill the zombie
Correct me if I'm wrong, but are you not setting the drop chance to 0.085? the HandDropChances specifies the chance for both hands. The 1.0 is being set for the other hand.