Network lifetime and energy consumption of data transmission have been primary Quality of Service (QoS) obligations in Wireless Sensor Networks (WSNs). The environment of a WSN is often organized into clusters to mitigate the management complexity of such obligations. However, the distance between Sensor Nodes (SNs) and the number of clusters per round are vital factors that affect QoS performance of a WSN. A designer's conundrum resolves around the desire to sustain a balance between the limited residual energy of SNs and the demand for prolonged network lifetime. Any imbalance in controlling such objectives results in either QoS penalties due to draining SN energies, or an over-cost environment that is significantly difficult to distribute and operate. Low-Energy Adaptive Clustering Hierarchy (LEACH) is a distributed algorithm proposed to tackle such difficulties. Proposed LEACH-based algorithms focus on residual energies of SNs to compute a probability function that selects cluster-heads and an optimal energy-efficient path toward a destination SN. Nevertheless, these algorithms do not consider variations in network's state at run-time. Such a state changes in an adaptive manner according to existing network structures and conditions. Thus, cluster-heads per round are not elected adaptively depending on the state and distances between SNs. This paper proposes an energy-efficient adaptive distance-based clustering called Adapt-P, in which an adaptive probability function is developed to formulate clusters. A near-optimal distance between each cluster-head and its cluster-members is formulated so that energy consumption of the network is mitigated and network lifetime is maximized. The cluster-head selection probability is adapted at the end of each round based on the maximum number of cluster-heads permitted per round found a priori and the number of alive SNs in the network.