Links are broken after changing the BaseURL

Looks very similar to CONFSERVER-52060.

Is reproducing on Confluence 6.7.3, 6.8.4, 6.9.1

Steps to reproduce

1. Set up Confluence instance
2. Create a few pages and another page with links to the other pages.
3. Shut down Confluence, add a context path, and bring up Confluence again.
4. Update BaseURL
5. Edit and save the page before without making any changes.
6. All links in the page link back to that page itself, and in my case, the text becomes *Link"