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As more distributed energy resources are deployed into distribution networks, supply and demand matching between prosumers becomes a new challenge for distribution system operators (DSOs) due to the intermittency of DERs. Recent studies begin to expand the responsibilities of DSOs towards local generation and consumption optimization, such as establishing a flexible local market. However, the difficulty of boosting local power exchange while reducing operation costs still remains unsolved. In this article, we propose a new way of power trading management for DSOs from a brokerage perspective. Specifically, DSOs endeavor to coordinate prosumers in the local market by setting a fair transactive price as incentive signals. Meanwhile, to compensate for the operation cost (e.g., power line loss), DSOs need to charge commission. We investigate how to compute the optimal transactive price in a privacy-preserving way by using a distributed algorithm and set a fair service fee, which attracts more power transactions in the local market as well as reduces the operation cost of DSOs. Moreover, to accelerate the distributed algorithm, we derive an optimal transactive price updating rule for DSOs, and the closed-form expression of the optimal strategy for each prosumer with respect to the transactive price. Numerical results on Southern California Edison 56-bus feeder and IEEE 123-node test feeder show that the proposed power trading management for DSOs from a brokerage perspective leads to a TRIPLE win. With the proposed mechanism, the prosumers' payoffs largely increase by as much as 192.85%. Then, the prosumers are more willing to exchange power locally, which significantly reduces the increasing transmission burden in transmission networks of power systems. Moreover, DSOs obtain compensation by charging a service commission and reduce their operating costs.