This paper studies spatial capacity in a stochastic wireless ad hoc network, where multi-stage probing and data transmission are sequentially performed. We propose a novel signal-to-interference-ratio (SIR) threshold based scheduling scheme, where by starting with the first probing, each transmitter iteratively decides to further probe or stay idle, depending on whether the estimated SIR in the proceeding probing is larger or smaller than a predefined threshold. Although one can assume that the transmitters are initially deployed according to a homogeneous Poisson point process (PPP), the SIR based scheduling makes the PPP no longer applicable to model the locations of retained transmitters in the subsequent probing and data transmission phases, due to the interference induced coupling in their decisions. We first focus on single-stage probing and find that when the SIR threshold is set sufficiently small to assure an acceptable interference level in the network, the proposed scheme can greatly outperform the non-scheduling reference scheme in terms of spatial capacity. We clearly characterize the spatial capacity and obtain exact/approximate closed-form expressions, by proposing a new approximate approach to deal with the correlated SIR distributions over non-Poisson point processes. Then we successfully extend to multi-stage probing by properly designing the multiple SIR thresholds to assure gradual improvement of the spatial capacity. Furthermore, we analyze the impact of multi-stage probing overhead and present a probing-capacity tradeoff in scheduling design. Finally, extensive numerical results are presented to demonstrate the performance of the proposed scheduling as compared to existing schemes.