I am wondering what algorithm does google use to make chrome browser\'s address bar to act as a default search bar for many websites like SO, Quroa etc. but not for facebook, me
Chrome uses search engines mechanism. It is described here how to use it http://support.google.com/chrome/bin/answer.py?hl=en&answer=95653&topic=14676&ctx=topic
Chrome automatically identifies search boxes and adds corresponding rules to search engines list. Maybe it's engine relies on document parsing. Hense a particular site may be added or not because of it's search box markup. https://superuser.com/questions/276069/google-chrome-automatically-adding-websites-to-my-list-of-search-engines
If you want to know about parsing algorithm, the only way i see is to dig through chrome sources
Also, you can edit search engine list manually.
PS: And it's not only chrome's feature, other browsers have similar things. Opera as an example http://tech.gaeatimes.com/index.php/archive/how-to-easily-use-manage-your-search-engines-in-opera-browser/