This paper studies the constrained-space probabilistic threshold range query (CSPTRQ) for moving objects. We differentiate two kinds of CSPTRQs: implicit and explicit ones. Specifically, for each moving object \(o\), we assume \(o\) cannot be located in some specific areas, we model its location as a closed region, \(u\), together with a probability density function, and model a query range, \(R\), as an arbitrary polygon. An implicit CSPTRQ can be reduced to a search (over all the \(u\)) that returns a set of objects, which have probabilities higher than a probability threshold \(p_t\) to be located in \(R\), where \(0\leq p_t\leq 1\). In contrast, an explicit CSPTRQ returns a set of tuples in form of (\(o\), \(p\)) such that \(p\geq p_t\), where \(p\) is the probability of \(o\) being located in \(R\). A straightforward adaptation of existing method is inefficient due to its weak pruning/validating capability. In order to efficiently process such queries, we propose targeted solutions, in which three main ideas are incorporated: (1) swapping the order of geometric operations based on the computation duality; (2) pruning unrelated objects in the early stages using the location unreachability; and (3) computing the probability using the multi-step mechanism. Extensive experimental results demonstrate the efficiency and effectiveness of the proposed algorithms.