Incapability is the state of not being able to do something. It is the noun that sits beside incapable. It is rather formal, and in real speech and writing inability is the word you will meet far more often: inability to sleep, inability to pay. Use incapability when you are matching the adjective incapable, or in cold official prose. Though actually, English also has incapacity, which often means a legal or medical lack of power to act — a more specialised neighbour, not a synonym you can swap in freely. In everyday talk, just say cannot.

沒有能力；無能（此詞較書面。中文「無能」常像在罵人；英文 incapability 本身較中性、正式。日常較常說 inability。）