Using the relational coarsest partition (RCP) method, this article aims to study the observability problem of probabilistic Boolean networks (PBNs). The key step to solving this problem is to find the parallel cycle and the coarsest refinement partition of the given initial partition. Firstly, several definitions of observability for PBNs are proposed, and the connections between finite-time observability with positive probability (FTOPP), asymptotical observability (AO), and finite-time observability with probability one (FTOPO) are revealed. Secondly, by defining the appropriate transition relation, the RCP method is introduced into PBNs. In addition, based on the output signal mapping set, the initial partition is constructed. Thirdly, the concept of a parallel cycle for PBNs is proposed, and two algorithms are presented for computing the cycle and parallel cycle of PBNs. Moreover, with the help of the RCP method, a series of criteria are derived to solve the observability problem of PBNs, which works more efficiently. Fourth, when PBN is unobservable, an algorithm is proposed to design the state-flipping set with the smallest number of states, which can make the unobservable PBN observable. To show the validity and effectiveness of the obtained results, examples are finally given.