Latency-sensitive applications, such as online gaming, require that the conditions of networks from the server to each client are almost the same to achieve fairness. Traditionally, the servers are always set fixedly in certain locations and only the nearby clients can connect, which is not fair to some far-away clients. To tackle the fairness issue, the emerging cloud computing or sky computing is a potential solution, where the server cannot be fixed anymore. Hence, we design LibraCloud, a novel server selection and allocation mechanism for latency-sensitive applications, using globally distributed cloud infrastructure. LibraCloud aims to select the fairest server rather than the best one. By defining a fairness indicator and dynamically utilizing multiple clouds, it overcomes the limitations of traditional fixed servers. To validate LibraCloud, we conduct experiments using 85 probes to simulate clients and 13 data centers for server selection. Assuming 20 distributed clients, 78.8% of the experimental cases show that LibraCloud selects the fairest server, significantly outperforming random selection or fixed three-server mechanisms.