How to calculate NDCG in recommendation system
IMHO,
The fundamental definition of DCG is that it is a measure of ranking quality. This assumes that you have computed the utilities of each document/item and ranked them in a certain order.
With this definition in mind, if you have n-items with same utility (which is 0 in your case), computing NDCG to measure the ranking quality within this subset of items (since you are only looking at items 5, 4, 3, 2 and 1, all of which are not recommended), will yield you a NDCG score of 1 - since your ranking is perfect if you are only looking at these items.
NDCG is merely a way to quantify the quality of ordering, i.e., current order Vs perfect order (items sorted w.r.to their utilities). This is meaningless if you are looking ONLY at items with same utility score.
I hope this answers your question.