I think you will need to have a look at Ajax in javascript. These allow you to get information remotely but you will need to use more javascript to empty and then populate the dropbox. The Ajax call will interact with the PHP code which then talks with the database. I suggest you raise this in the PHP or javascript forum.
Here is an example of Ajax in action:
errno
You add in the errno value and it will search in the database for the corresponding text without ever moving from the web page. The javascript takes the returning text, empties the results area and then applies the returned text string in the results area.