No player can look at the cards once they’re exiled.

If your opponent puts one of the face-down exiled cards into your graveyard (for example, to activate an ability of an Eldrazi Processor), choose one of the cards at random. The card is revealed only after the cost is fully paid. That is, your opponent can’t learn what card was chosen and decide to back up (not cast the spell, activate the ability, or so on, as applicable).