### A Bayesian interpretation of Holmesian deduction

An interesting point I’ve read from book “Doing Bayesian Data Analysis“, is the Bayesian interpretation of the famous deduction from Sherlock Holmes: ” How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?”. In other words,

How often have I said to you that when $p(D|\theta_i)=0$ for all $i\neq j$, then, no matter how small the prior $p(\theta_j)>0$ is, the posterior $p(\theta_j|D)$ must equal one.