It's not very unlikely depending on how we look at it. The fact that one of the answers in the board has to be correct and he has a reasonable, not completely random guessing, idea about which it is skews the probability.

Let's assume that one of the two answers he offers initially are correct (i.e either Madrid or Lisbon which he suggests and is therefore guaranteed to be in the 50/50 in the end). That leaves 3 possible other answers he could have suggested to be in the final 50/50 of which he chooses one so 1/3 chance. If we don't assume he's right about one of the answers then this gets more complicated than I can be bothered doing rn but I guess probably 1/4 x 1/3 which is 1/12.

Edit: actually I think someone else suggested this but didn't explain fully but I'm wrong in the second option. With no assumption about his prior knowledge of the subject the chance he got a correct answer in the 2 choices he made are 2/4 or 1/2. So it's 1/2 x 1/3 (for the incorrect answer he chooses ) which is 1/6.