If all chosen targets are illegal as Electrolyze tries to resolve, it won't resolve and none of its effects will happen. No damage will be dealt and you won't draw a card.

You divide the damage as you cast Electrolyze, not as it resolves. Each target must be assigned at least 1 damage. In other words, as you cast Electrolyze, you choose whether to have it deal 2 damage to a single target, or deal 1 damage to each of two targets.

If Electrolyze targets two creatures and one becomes an illegal target, the remaining target is dealt 1 damage, not 2. You'll still draw a card.