To address the challenge of fault diagnosis for a rotary steerable drilling tool system under scenarios with unknown fault prior assumption, this paper proposes an intelligent fault diagnosis method that integrates probabilistic Transformer with particle filter. First, aiming at the inherent drawbacks of traditional particle filter, including constrained particle sampling capability and particle degeneracy under the condition of missing fault priors, the nonlinear singular system is constructed by introducing an augmented vector that includes system states and sensor faults. A well-trained probabilistic Transformer is used to generate conditional probability distributions for particle sampling of the singular system, while measurement data are leveraged to optimize the importance sampling distribution of the particle filter, thereby alleviating particle degeneracy and achieving joint estimation of system states and faults. Then, statistical properties of the estimation results are analyzed, leading to the development of a residual evaluation function that approximates the $\chi^{2}$ distribution. By implementing the moving average strategy to optimize the fault detection algorithm, the method significantly reduces the missed detection rate of fault detection. Finally, through simulation verification and experimental analysis on the rotary steerable drilling tool system, the effectiveness of the proposed fault diagnosis method is validated, and results indicate that it can enhance diagnostic accuracy and lower computational costs.