After years of hunting on Arkarium boss (Normal mode), I think I want to drop my final conclusion here for the drop rate of confusion fragment. All of players known this etc item as 'CF' which worth 1.6b each.
It is used to craft items such as meister earring, and more. However, it is super duper rare etc item. Currently this is the rarest etc item in the game. Here is my experience, I killed Arkarium everyday, every 3~6 months I will get 1 CF with 180% drop rate.
6 months = 30 days * 6 = 180 days.
So the longest I took to get a CF is 180 days! This is how rare this etc is....
Sometimes, you will get 1 CF after 3 months of killing Arkarium. But it is still super super rare... this etc item is more common than dominator pendant but it is still very rare this is why it is worth 1.6b each.
If you are hunting for CF, or you want to know how rare is CF, above is the answer above answered by me.