A framework for the probabilistic finite element model updating based on measured modal data is presented. The described framework is applied to a seven-storey building made of cross-laminated timber panels. The experimental estimates based on the forced vibration test are used in the process of model updating. First, a generalized Polynomial Chaos surrogate model is derived representing the map from the model parameters to the eigenfrequencies and the eigenvectors. To overcome the difficulties caused by mode switching, we propose a novel approach to mode tracking based on partitioning an extended and low-rank representation of the mode shapes resulting from different setups of the finite element model into clusters by the k-means clustering algorithm. Second, the surrogate model derived with the help of mode pairing is used to efficiently perform sensitivity analysis and uncertainty quantification of the first five frequencies and the corresponding mode shapes. Finally, the surrogate-based Bayesian update of the model parameters is efficiently performed, providing engineers not only with a finite element model that gives a good fit to the experimental modal data, but also a stochastic model that represents the uncertainties originating from the initial model and the uncertainties of measuring modal properties.