I control an Alms Collector, and a Narset, Parter of Veils. I cast a Wheel of Fortune. What happens?

Do I draw 7 or 8 cards? I know my opponent will only draw one, and that if they have somehow already drawn a card this turn, there will be no event to replace, but does Alms Collector replace the instruction to draw 7 cards, even though it is not possible to do? Does 614.17c (If an event can't happen, it can only be replaced by a self-replacement effect (see rule 614.15). Other replacement and/or prevention effects can't modify or replace it.) apply or not?

Edited Jeff S Higgins (June 15, 2019 12:29:52 PM)