Topple some dominoes!
Retina, 32 bytes

+`(/.\\)|(/)\||\|(\\)
$1$2$2$3$3


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Explanation

The + tells Retina to run the replacement in a loop until it fails to change the string. Each replacement computes one step the falling dominoes. The replacement itself is really three replacements in one, but this ensures that they happen simultaneously:

(/.\\)...
$1


This just matches /|\ (as well as /\\ and /\\, but those don't matter) and reinserts it unchanged. The purpose of this is to skip over | with fallen dominoes on both sides, because this is shorter than ruling out those cases with separate lookarounds in the other two cases.

...(/)\|...
$2$2


This matches /| and turns it into //.

...\|(\\)
$3$3


This matches |\ and turns it into \\.