Many previous studies regarding the theoretical models of social dilemmas have described that rewarding opponents can help players to cooperate with each other. Those studies deal with reward not for defectors, but for cooperators. However, many prior researches concerning punishment that is also considered to be necessary for the evolution of cooperation discuss punishment on cooperators as well as defectors. Considering the group level, defectors who have too much payoff due to many cooperators around them will lose their superiority over cooperators by rewarding not only cooperators but also defectors surrounding them. As a result, cooperation among players can be realized.Therefore, this study proposes the new universal probabilistic reward based on the difference of payoff, where the greater the payoff of each player is, the higher the probability of giving reward to their opponents becomes regardless of the strategy of their opponents. This paper shows that by introducing the reward of this study into the framework of the spatial prisoner's dilemma game utilized in previous studies, the high-level evolution of cooperation can be achieved especially in both the relatively sparse regular and scale-free topology of connections. In addition, the programming method utilized to construct the simulator for this study will serve as teaching materials for specialized education at Kanagawa Institute of Technology.