Multi-section license plate recognition (LPR) data provides input-output information and sampled travel times of the investigated link, serving as an ideal data source for lane-based queue length estimation in recent studies. However, most of these studies assumed the strict FIFO rule or a specific arrival process, thus ignoring the potential impact of overtaking and the variation of traffic flows, especially in multi-lane scenarios. To address this issue, we propose a probabilistic approach to derive the stochastic queue length by constructing a conditional probability model of no-delay arrival time (NAT), i.e., the arrival time of vehicles without experiencing any delay, based on multi-section LPR data. First, the NAT conditions for all vehicles are established based on upstream and downstream vehicle departure times and sequences. To reduce the computational dimensionality and complexity, a DP-based algorithm is developed for vehicle group partitioning based on potential interactions between vehicles. Then, the conditional probability of NATs of each vehicle group is derived and an MCMC sampling method is employed for calculation. Subsequently, the stochastic queue profile and maximum queue length for each cycle can be derived based on the NATs of vehicles. Eventually, to leverage the LPR data sufficiently, we extend our approach to multi-lane scenarios, where the problem can be converted to a weighted general exact coverage problem and solved by a backtracking algorithm with heuristics. Empirical and simulation experiments have shown that the proposed approach outperforms the state-of-the-art method, demonstrating significant improvements in accuracy and robustness across various traffic conditions, including different V/C ratios, matching rates, and FIFO violation rates. In addition, the performance of the proposed approach can be further improved by utilizing multi-lane LPR data.