Small bit of UI inconsistency here: on the abilities screen, under “Cost” for invisibility it says Drain, which makes sense.
But then when you choose to describe it, it says “This ability costs: nothing.” followed by a detailed description of the cost it does actually have(HP drain).
Obviously this is because that first line lists a mana cost. But for something like this on the description screen, either the first contradictory line saying it costs nothing should be removed, or after the colon it should say “HP drain” or something like that and then the second line removed.