In computational social science, epidemic-inspired spread models have been widely used to simulate information diffusion. However, recent empirical studies suggest that simple epidemic-like models typically fail to generate the structure of real-world diffusion trees. Such discrepancy calls for a better understanding of how information spreads from person to person in real-world social networks. Here, we analyse comprehensive diffusion records and associated social networks in three distinct online social platforms. We find that the diffusion probability along a social tie follows a power-law relationship with the numbers of disseminator's followers and receiver's followees. To develop a more realistic model of information diffusion, we incorporate this finding together with a heterogeneous response time into a cascade model. After adjusting for observational bias, the proposed model reproduces key structural features of real-world diffusion trees across the three platforms. Our finding provides a practical approach to designing more realistic generative models of information diffusion.