This paper investigates the problem of joint transmission and computation resource allocation for a multi-user probabilistic semantic communication (PSC) network. In the considered model, users employ semantic information extraction techniques to compress their large-sized data before transmitting it to a multi-antenna base station (BS). The model represents large-sized data through substantial knowledge graphs, utilizing shared probability graphs between the users and the BS for efficient semantic compression. The resource allocation problem is formulated as an optimization problem with the objective of maximizing the sum of equivalent rate of all users, considering total power budget and semantic resource limit constraints. The computation load considered in the PSC network is formulated as a non-smooth piecewise function with respect to the semantic compression ratio. To tackle this non-convex non-smooth optimization challenge, a three-stage algorithm is proposed where the solutions for the receive beamforming matrix of the BS, transmit power of each user, and semantic compression ratio of each user are obtained stage by stage. Numerical results validate the effectiveness of the proposed scheme. The key contributions of this work include the development of a multi-user PSC framework that jointly considers transmission and computation consumption, the formulation of an optimization problem to maximize the sum equivalent rate of all users, and the proposal of a low-complexity three-stage algorithm to solve the non-convex non-smooth optimization problem. The algorithm consists of three stages: MMSE for receive beamforming matrix, rough search for semantic compression ratio, and refined search for semantic compression ratio. The results show that the proposed algorithm achieves a higher sum of equivalent rate compared to other schemes.This paper investigates the problem of joint transmission and computation resource allocation for a multi-user probabilistic semantic communication (PSC) network. In the considered model, users employ semantic information extraction techniques to compress their large-sized data before transmitting it to a multi-antenna base station (BS). The model represents large-sized data through substantial knowledge graphs, utilizing shared probability graphs between the users and the BS for efficient semantic compression. The resource allocation problem is formulated as an optimization problem with the objective of maximizing the sum of equivalent rate of all users, considering total power budget and semantic resource limit constraints. The computation load considered in the PSC network is formulated as a non-smooth piecewise function with respect to the semantic compression ratio. To tackle this non-convex non-smooth optimization challenge, a three-stage algorithm is proposed where the solutions for the receive beamforming matrix of the BS, transmit power of each user, and semantic compression ratio of each user are obtained stage by stage. Numerical results validate the effectiveness of the proposed scheme. The key contributions of this work include the development of a multi-user PSC framework that jointly considers transmission and computation consumption, the formulation of an optimization problem to maximize the sum equivalent rate of all users, and the proposal of a low-complexity three-stage algorithm to solve the non-convex non-smooth optimization problem. The algorithm consists of three stages: MMSE for receive beamforming matrix, rough search for semantic compression ratio, and refined search for semantic compression ratio. The results show that the proposed algorithm achieves a higher sum of equivalent rate compared to other schemes.