Rule mining in knowledge graphs enables interpretable link prediction. However, deep learning-based rule mining methods face significant memory and time challenges for large-scale knowledge graphs, whereas traditional approaches, limited by rigid confidence metrics, incur high computational costs despite sampling techniques. To address these challenges, we propose MPRM, a novel rule mining method that models rule-based inference as a Markov chain and uses an efficient confidence metric derived from aggregated path probabilities, significantly lowering computational demands. Experiments on multiple datasets show that MPRM efficiently mines knowledge graphs with over a million facts, sampling less than 1% of facts on a single CPU in 22 seconds, while preserving interpretability and boosting inference accuracy by up to 11% over baselines.