How in the world are you going to measure the intrinsic difficulty of a chess problem? That's actually a non-sensical notion... chess problems are only difficult, or easy, to or for a chess player. There is literally no intrinsic difficulty, there is only relational difficulty.
One way would be to use a chess engine to rate the value of each possible move. The more moves there are that are close in value to the "optimal" move, the more difficult the position would be to assess.
If there is only one or two good moves, then that is a much easier proposition.
That's one possible way, I guess

Paradox's idea that positions have some inherent difficulty strikes me as a common sense idea, and I agree with him that's a way for experienced chess players to spot cheaters.
I mean, say you play with some 8 y.o. kid : would you expect him to be able to play a rook endgame with the same patience and skill than a veteran player ? Or would you expect any chess player to find a combo such as this one ?