Well, I got curious about the probability to see an item appearing in a dungeon, so I calculated the probabilities for every item (all items unlocked, no preparations, no veto, 8 shops):
EDIT:
Wondering about the influence of removing items and adding a shop. Note, that you have to insert the items yourself, depending on which were removed (either by vetoing or by prepping it).
all items unlocked, 4 items removed, 8 shops:
all items unlocked, 8 removed, 9 shops: