Is it possible to get a list of files under a directory of a website? How?

DirBuster is such a hacking script that guesses a bunch of common names as nsanders had mentioned. It literally brute forces lists of common words and file endings (.html, .php) and over time figures out the directory structure of such sites, this could discover the page as you described but would also discover many others.

Any crawler or spider will read your index.htm or equivalent, that is exposed to the web, they will read the source code for that page, and find everything that is associated to that webpage and contains subdirectories. If they find a "contact us" button, there may be is included the path to the webpage or php that deal with the contact-us action, so they now have one more subdirectory/folder name to crawl and dig more. But even so, if that folder has a index.htm or equivalent file, it will not list all the files in such folder.

If by mistake, the programmer never included an index.htm file in such folder, then all the files will be listed on your computer screen, and also for the crawler/spider to keep digging. But, if you created a folder www.yoursite.com/nombresinistro75crazyragazzo19/ and put several files in there, and never published any button or never exposed that folder address anywhere in the net, keeping only in your head, chances are that nobody ever will find that path, with crawler or spider, for more sophisticated it can be.

Except, of course, if they can enter your FTP or access your site control panel.