Markdown not working on old comments

I transitioned a site to a new WordPress site and noticed that there are bunch of comments that have markdown in them, but that they are not in markdown (but rather in an unprocessed format ie *comment*).

How can I get all the old comments to be processed in Markdown to appear properly.

Website: http://www.thebookdesigner.com/
example post comments:
http://www.thebookdesigner.com/2013/10/where-can-i-legally-use-my-fonts/

http://www.thebookdesigner.com/2013/10/book-design-curriculum/

http://www.thebookdesigner.com/2013/06/top-5-errors/

https://wordpress.org/plugins/jetpack-markdown/