Matticus, Orathaic explained it perfectly above.
To elaborate, the odds of a player drawing "any" country two times in a row are simply the odds that the first country drawn (which is a 100% probability, because there is 100% chance that you will get one of the 15 countries when you sign up for a game) is now drawn again, so 1 * 1/15 = 1/15.
Now, this is why you are probably confused, Matticus. If you had to bet money BEFORE you drew the first country that you would draw a SPECIFIC country (let's say France) two times in a row, then your odds of winning that bet would only be 1/15 * 1/15 = 1/225. This is because the first country you draw could also be Spain, Turan, India, or one of any 14 countries other than France, but you don't win the bet if Spain, Turan or India are drawn two times in a row. You only win if France is drawn two times in a row. No odds maker would let you make the bet after the first half of the results are in.
But this is not what your "bug" question suggests. You are thinking there is a bug because you drew "any" country two times in a row. That will happen quite often, or 1 in 15 times.
Now the chance of drawing "any" country THREE times in a row would be 1 * 1/15 * 1/15 = 1/255. So, draw the same country again, one more time, and then you'll have reached your 1/255 probability. If that starts happening to a lot of players, and not just to you, over a short period of time, then perhaps there is a bug.