Is there a word to describe the state of believing you know something that is false?

Solution 1:

One word is mistaken.

adjective
  wrong in one’s opinion or judgement:
    she wondered whether she’d been mistaken about his intentions
      based on or resulting from a misunderstanding or faulty judgement:
        don’t buy a hard bed in the mistaken belief that it is good for you
        an unfortunate case of mistaken identity

[ODO]

Solution 2:

Such a belief could be described as erroneous. Merriam-Webster defines erroneous as "containing or characterized by error: mistaken."

Solution 3:

I think that this example is merely a matter of ignorance: the person who believes that there is a rabbit in the box is ignorant of the fact that the rabbit was removed and, therefore, continues to believe something that once was true but has since changed and become false.

A better word than ignorant and mistaken, I think, is one of these:

tricked, bamboozled, conned, deceived, duped, misled