Conformance checking techniques are usually used to determine to what degree a process model and real execution trace correspond to each other. Most of the state-of-the-art techniques to calculate conformance value provide an exact value under the circumstance that the reference model of a business system is known. However, in many real applications, the reference model is unknown or changed for various reasons, so the initial known reference model is no longer feasible, and only some historical event execution traces with its corresponding conformance value are retained. This paper proposes a log drivened conformance checking method, which tackles two perspective issues, the first is presenting an approach to calculate the approximate conformance checking value much faster than the existing methods using machine learning method. The second is presenting an approach to conduct conformance checking in probabilistic circumstances. Both kinds of approaches are from the perspective of no reference model is known and only historical event traces and their corresponding fitness can be used as train data. Specifically, for large event data, the computing time of the proposed methods is shorter than those align-based methods, and the baseling methods includes k-nearest neighboring, random forest, quadratic discriminant analysis, linear discriminant analysis, gated recurrent unit and long short-term memory. Experimental results show that adding a machine learning classification vector in the training set as preprocessing for train data can obtain a higher conformance checking value compared with the training sample without increasing the classification vector. Simultaneously, when conducted in processes with probabilities, the proposed log-log conformance checking approach can detect more inconsistent behaviors. The proposed method provides a new approach to improve the efficiency and accuracy of conformance checking. It enhances the management efficiency of business processes, potentially reducing costs and risks, and can be applied to conformance checking of complex processes in the future.