In recent years, indoor positioning systems (IPSs) have received attention from many research fields, such as robotics, navigation, human-computer interaction, etc. However, IPS based on passive radio frequency (PRF) technology is still rare. This paper proposes an three-dimensional (3D) IPS based on received signal strength (RSS) distribution and Gaussian process regression (GPR). Traditional RSS-based positioning systems have a transmitter with known frequencies, while in the proposed PRf signal of Opportunity - 3D IPS (PRO-3DIPS), the system neither deploys new transmitters nor uses any a priori knowledge of transmitters. Furthermore, PRO-3DIPS integrates multiple Signal of Opportunity (SoOP) sources, shadowing, fading, and also captures scenario signatures. Data collection and analysis of PRF-based RSS distribution in 3D space enables the capability of 3D positioning. Three methods are applied and compared to find the frequency band most impacted by the scenario to achieve the best positioning performance as well as used in the estimation of RSS distribution. The RSS distribution is estimated by measuring the PRF spectrum on a fixed grid in the scenario. Using the RSS distribution, the GPR can accurately locate the receiver position. RSS at 90-gridded positions were collected in the experiment scenario, with one hundred samples at each position. The experimental result shows that a root mean square error (RMSE) of the proposed PRO-3DIPS is 0.292 meters when the sampling distance is 1 meter. The result demonstrates that the PRF spectrum is a new modality for the positioning task, which demonstrates better performance than most existing RF-based technologies.