Detection of out-of-distribution (OOD) samples is crucial for safe real-world deployment of machine learning models. Recent advances in vision language foundation models have made them capable of detecting OOD samples without requiring in-distribution (ID) images. However, these zero-shot methods often underperform as they do not adequately consider ID class likelihoods in their detection confidence scoring. Hence, we introduce CLIPScope, a zero-shot OOD detection approach that normalizes the confidence score of a sample by class likelihoods, akin to a Bayesian posterior update. Furthermore, CLIPScope incorporates a novel strategy to mine OOD classes from a large lexical database. It selects class labels that are farthest and nearest to ID classes in terms of CLIP embedding distance to maximize coverage of OOD samples. We conduct extensive ablation studies and empirical evaluations, demonstrating state of the art performance of CLIPScope across various OOD detection benchmarks.