Comprehension algorithms like High Efficiency Video Coding (HEVC) facilitates fast and efficient handling of multimedia contents. Such algorithms involve various computation modules that help to reduce the size of content but preserve the same subjective viewing quality. However, the brute-force behavior of HEVC is the biggest hurdle in the communication of multimedia content. Therefore, a novel method will be presented here to accelerate the encoding process of HEVC by making early intra mode decisions for the block. Normally, the HEVC applies 35 intra modes to every block of the frame and selects the best among them based on the RD-cost (rate-distortion). Firstly, the proposed work utilizes neighboring blocks to extract available information for the current block. Then this information is converted to the probability that tells which intra mode might be best in the current situation. The proposed model has a strong foundation as it is based on the probability rule-2 which says that the sum of probabilities of all outcomes should be 1. Moreover, it is also based on optimal stopping theory (OST). Therefore, the proposed model performs better than many existing OST and classical secretary-based models. The proposed algorithms expedited the encoding process by 30.22% of the HEVC with 1.35% Bjontegaard Delta Bit Rate (BD-BR).