Causal Bayesian Network is a class of causal models with many applications in statistics and machine learning. With nodes denoting random variables, it takes a directed acyclic graph (DAG) as a compact and intuitive representation of the causal relationships among those random variables. We call such a DAG causal structure and a probability distribution P compatible with a causal structure G if P factorizes according to the graphical structure of G. Given a causal structure G with latent variables and a probability distribution P on observed variables, a difficult task is to verify whether P is compatible with G. Wolfe et al. (2019) proposed a so-called inflation technique to derive necessary conditions for a probability distribution to be compatible with a causal structure. It is then proved by Navascués and Wolfe (2020) that the inflation technique is also complete. In this talk, I will give an introduction to the inflation technique for causal compatibility problem and prove the completeness result via a generalized version of the finite de Finetti theorem, which may be of independent interest for probability theory itself.