I have a question regarding the use of commas when writing probabilities. In the following statement of the law of total probability for conditional probabilities, commas are used to describe unions, however the "order" of these unions isn't very clear.
On the last line, when $P(A|B_n,C)$ is written, how do we know if this means $P(A| (B_n \cap C))$ or $P((A|B_n) \cap C)$ ? Is there a specific rule for using commas in a certain way?