In the computation of precision@k, we are dividing by the number of items recommended in the top-k recommendation. If there are no items recommended. i.e. number of recommended items at k is zero, we cannot compute precision at k since we cannot divide by zero.
Evaluation measures for an information retrieval system are used to assess how well the .... measure, because recall and precision are evenly weighted. .... Precision at k documents (P@k) is still a useful metric (e.g., P@10 or "Precision at 10"
C K Gomathy: Please correct me if I am wrong. For precision@k (P@k), where k is the position in the retrieval list, thus if the number of recommended items at k is zero then the value of P@k is zero. As we divide the number of recommendations by the value of k.