This study explores the application of deep learning to diagnose glaucoma using retinal fundus images, addressing the increasing global prevalence of this condition. Utilizing the EfficientNetV2B0 neural network model, trained on the RIM One dataset of 485 optic disc images, the study achieved an area under the curve (AUC) of 96%, with sensitivity, specificity, positive predictive value, and negative predictive value of 91%, 99%, 98%, and 95%, respectively. A novel approach in this research involves the use of a 95% prediction probability threshold to enhance clinical relevance. For images with high predictive confidence, the AUC improved to 100%, with perfect sensitivity and specificity. This method aligns with clinical practices, ensuring further investigation only when high confidence in diagnosis is achieved. The DeLong t-test indicated statistically significant improvements in AUC, sensitivity, and negative predictive value for high-confidence predictions compared to the broader test set. This study is the first to incorporate prediction probability into AI models for glaucoma diagnosis, suggesting a practical tool for efficient and accurate screening in clinical settings.