Study Problem

I'm sure any number of individuals who like to argue will be along to make tortured distinctions, but really, there isn't any significant difference between them. Forbid is often a reference to a command from an individual--"I forbid you to go out with those people." But it is also used passively: "Drinking in public is forbidden." In passive constructions, there really is no difference in the three.

Oh,yes.I know , think you !

Oxford dictionary tells me that prohibit refers to formally forbid (something) by law, rule, or other authority.
It is an important clue to recognize that forbid is more casual than prohibit. Forbid just means refuse to allow (something).

Any lexicographers care to comment?

It is best to seek the advice of native speakers with a wide experience of literature in the English language--as opposed to those who are not native speakers and who have only a very limited experience of English literature.

Forbid: to order sb not to do sth (forbid sb. to do sth.）
e.g. The regulations forbids the carrying mobile phones into the testing rooms.
The mother forbade her child to swim in the river unless someone agrees to watch over.

Prohibit: to stop sth from being done or used especially by law (prohibit sb.from sth/doing sth.)
e.g. Shops and supermarkets are prohibited from offering free plastic bags.
In some countries private citizen are prohibited from carrying and using guns and firearms.

Ban: to decide or say officially that sth is not allowed (ban ...from sth./doing sth.)
e.g. Canada will ban smoking in all offices later this year.
He was banned from driving for three years.

Forbid and prohibit are like orders not to do something. It is up to you to follow it or not. But banning something is something like a law passed by governing bodies to forbid people to do that thing. So if you are participating in banned activities, you are breaking the law. Well, this is my opinion on difference between ban and prohibit/forbid. Others can think differently.