The St. Petersburg Paradox (SPP), where people are willing to pay only a modest amount for a lottery with infinite expected gain, has been a famous showcase of human (ir)rationality. Since inception multiple solutions have been proposed, including the influential expected utility theory. Criticisms remain due to the lack of a priori justification for the utility function. Here we report a new solution to the long-standing paradox, which focuses on the probability weighting component (rather than the value/utility component) in calculating the expected value of the game. We show that a new Additional Transition Time (AT) based measure, motivated by both physics and psychology, can naturally lead to a converging expected value and therefore solve the paradox.