The evolutionary game theory has been widely used to study the evolution of cooperation in social dilemmas where imitation-led strategy updates are typically assumed. However, results of recent behavioural experiments are not compatible with the predictions based on the imitation dynamics, casting doubts on the assumption of the imitation-led updates and calling for alternative mechanisms of strategy updates. Although an aspiration-led update is often considered as an alternative to the imitation-led one, they are still similar in that both yield cooperation less abundant than defection in Prisoner's Dilemma games. While details of update rules can have significant impacts on the evolutionary outcomes and many variations in imitation-led updates are thus studied, there exist few alternatives in aspiration-led updates. We introduce a novel aspiration-led update mechanism (`Satisfied-Defect, Unsatisfied-Cooperate') that is psychologically intuitive and yields cooperation to be more abundant than defection in Prisoner's Dilemma games. Using analytical and numerical methods, we study and link the stochastic dynamics of it in finite populations and the deterministic dynamics of infinite populations.