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Differential Neural Architecture Search (NAS) requires all layer choices to be held in memory simultaneously; this limits the size of both search space and final architecture. In contrast, Probabilistic NAS, such as PARSEC, learns a distribution over high-performing architectures, and uses only as much memory as needed to train a single model. Nevertheless, it needs to sample many architectures, making it computationally expensive for searching in an extensive space. To solve these problems, we propose a sampling method adaptive to the distribution entropy, drawing more samples to encourage explorations at the beginning, and reducing samples as learning proceeds. Furthermore, to search fast in the multi-variate space, we propose a coarse-to-fine strategy by using a factorized distribution at the beginning which can reduce the number of architecture parameters by over an order of magnitude. We call this method Fast Probabilistic NAS (FP-NAS). Compared with PARSEC, it can sample 64% fewer architectures and search 2.1x faster. Compared with FBNetV2, FP-NAS is 1.9x - 3.5x faster, and the searched models outperform FBNetV2 models on ImageNet. FP-NAS allows us to expand the giant FBNetV2 space to be wider (i.e. larger channel choices) and deeper (i.e. more blocks), while adding Split-Attention block and enabling the search over the number of splits. When searching a model of size 0.4G FLOPS, FP-NAS is 132x faster than EfficientNet, and the searched FP-NAS-L0 model outperforms EfficientNet-B0 by 0.7% accuracy. Without using any architecture surrogate or scaling tricks, we directly search large models up to 1.0G FLOPS. Our FP-NAS-L2 model with simple distillation outperforms BigNAS-XL with advanced in-place distillation by 0.7% accuracy using similar FLOPS.