This paper proposes a novel approach for global localisation of mobile robots in large-scale environments. Our method leverages learning-based localisation and filtering-based localisation, to localise the robot efficiently and precisely through seeding Monte Carlo Localisation (MCL) with a deep-learned distribution. In particular, a fast localisation system rapidly estimates the 6-DOF pose through a deep-probabilistic model (Gaussian Process Regression with a deep kernel), then a precise recursive estimator refines the estimated robot pose according to the geometric alignment. More importantly, the Gaussian method (i.e. deep probabilistic localisation) and non-Gaussian method (i.e. MCL) can be integrated naturally via importance sampling. Consequently, the two systems can be integrated seamlessly and mutually benefit from each other. To verify the proposed framework, we provide a case study in large-scale localisation with a 3D lidar sensor. Our experiments on the Michigan NCLT long-term dataset show that the proposed method is able to localise the robot in 1.94 s on average (median of 0.8 s) with precision 0.75~m in a large-scale environment of approximately 0.5 km2.