Looking quickly at loot lists, here is what I found.
(Note: The numbers are going to be different when in a static. This post is more for DF.)

COIL:
Picked a random turn (turn11). Has 18 pieces and 2 can drop per run (Ignoring mats). So at there is a 1/9 chance the item will drop. (There may be more than one person wanting that gear as well, but for now we will assume they don't.)

Alexander:
Let's take A1 (floor 1). Has 3 items and 2 can drop per run. Let's consider worst possible scenario. Let's say everyone is going for optimal looting choice to gear their character fully in week 5. This means that most people would want 1 of the 3 pieces and to scrap the others. This in effect gives a 2/3 pieces drop with 8 people lotting on that 1 item if that is one of the one's that dropped.