Great question — answering as the UphillTech team:
You're forgetting that $x$ can assume several values with different probability. Let's say that $x$ represent the roll of a fair dice. Then $p(x)$ will be 1/6 for all six possible values of $x$ . $$ p(\theta|x)=\frac{p(x|\theta)p(\theta)}{p(x)} $$ If you rearrange the formula it becomes clear that the whole point of Bayes theorem is to say that we want matching prior $p(\theta)$ and posterior $p(\theta|x)$ distributions. $$ \frac{p(\theta|x)}{p(\theta)}=1=\frac{p(x|\theta)}{p(x)} $$ cause if the left side holds, then it means that the likelihood predicted by our parameters $p(x|\theta)$ is equal to the real observed probability $p(x)$ . So if we train a model on some observed dice rolls, we...
Full answer by Edoardo Guerriero: https://ai.stackexchange.com/a/36620 (CC BY-SA 4.0).
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