In a wireless sensor network (WSN), after gathering information, tiny sensor nodes need to transmit data to a sink. It is important to guarantee that each node can communicate with a sink. Due to the multi-hop communication of WSNs, an essential condition for reliable transmission is completely connectivity of a network. Adaptive or smart antenna (SA) techniques in WSNs have been a topic of active research in recent years. These techniques have been shown to be effective with respect to decreasing energy consuming via specified regions which are formed by the SA beams. In this paper, we propose a probabilistic technique to determine the network connectivity probability of the SA integrated WSN. We employ the geometric shape model to evaluate the network connectivity probability of the WSN using the SA beam specifications. The sensor node density to satisfy the desired network connectivity is determined in terms of the beam-width of the antenna array and node transmission range. The analytical results agree with the simulation results by less than 4.7 % error in the average.