This is the brief review on quantum-like modeling, quantum probability versus classical probability in cognition, psychology, decision making, and artificial intelligence. We describe the problems induced by using classical probability (CP) for mathematical formalization of decision making—paradoxes and probability fallacies. These problems are related to the violation of the formula of total probability (FTP) derived in CP: either violation of additive of probability or Bayes formula for conditional probability. Quantum probability (QP) generates FTP with additional interference term, the latter provides the right balance of experimental probabilities obtained in cognitive psychology, decision making, and artificial intelligence. We consider application of QP to model violation of the Savage Sure Thing Principle (the axiom of agents’ rationality in CP-based decision making) and the order and response replicability effects. We make comparison CP versus QP rationality and briefly consider coupling with social laser theory.