The feasibility of practical in-band full-duplex radios has recently been demonstrated experimentally. One way to leverage full-duplex in a network setting is to enable three-node full-duplex, where a full-duplex access point (AP) transmits data to one node yet simultaneously receives data from another node. Such three-node full-duplex communication however introduces inter-client interference, directly impacting the full-duplex gain. It hence may not always be beneficial to enable three-node full-duplex transmissions. In this paper, we present a distributed full-duplex medium access control (MAC) protocol that allows an AP to adaptively switch between full-duplex and half-duplex modes. We formulate a model that determines the probabilities of full-duplex and half-duplex access so as to maximize the expected network throughput. A MAC protocol is further proposed to enable the AP and clients to contend for either full-duplex or half-duplex transmissions based on their assigned probabilities in a distributed way. Our evaluation shows that, by combining the advantages of centralized probabilistic scheduling and distributed random access, our design improves the overall throughput by 3.16× and 1.44×, on average, as compared to half-duplex 802.11 and greedy downlink-uplink client pairing.