This paper studies a networked sensing system with multiple base stations (BSs), which collaboratively sense the unknown and random three-dimensional (3D) location of a target based on the target-reflected echo signals received at the BSs. Considering a practical scenario where the target location distribution is known a priori for exploitation, we aim to design the placement of the multiple BSs to optimize the networked sensing performance. Firstly, we characterize the posterior Cramér-Rao bound (PCRB) of the mean-squared error (MSE) in sensing the target's 3D location. Despite its complex form under networked sensing, we derive its closed-form expression in terms of the BS locations. Next, we formulate the BS placement optimization problem to minimize the sensing PCRB, which is non-convex and difficult to solve. By leveraging a series of equivalent transformations and the iterative inner approximation method, we devise an algorithm with polynomial-time complexity which is guaranteed to converge to a solution satisfying the Karush-Kuhn Tucker (KKT) conditions of the problem. Numerical results show that the proposed placement design significantly outperforms various benchmark designs.