For a simple case, use
func _ready():
randomize()
var probability : int = 10 # 1/10 chance
if (randi() % probability) == (probability - 1):
it_happened() # do something
For a multiple items (Array) I suggest you need two answers: whether you want to drop something at all (use example above) and if it happens, check which one
var items = ["First", "Second", "Third"] # your items
# first check if items exist, actually should be done before first query
if items.size() > 0 :
var idx : int = randi() % items.size() # item index
var item = items[idx] # do something with item
items.remove(idx) # at least remove it from array