You’ll discard three cards at random even if some other effect replaces your seven draws.

You discard your hand as part of Drastic Revelation’s effect, not as an additional cost. If you have no cards in hand at this point, you simply don’t discard any; the rest of the spell will still have its effect.

If there are fewer than seven cards left in your library, you’ll draw all the cards in your library, then you’ll discard three cards at random. Then you’ll lose the game as a state-based action.