See if these links help:
URL Rewriting with ASP.NET[
^]
URL rewriting ASP.NET[
^]
Also, the short URL doesn't contain any extensions so the IIS wouldn't be able to process it anyway and would throw a 404, to manage extensionless URLs you would need a third party ISAPI filter installed on the server side. However, if you are using IIS7 then an inbuilt tool called URLRewrite may be able to take care of that (not sure though). Plus, i would recommend using RegEx for path pattern matching which is how most URL rewriting engines work.
Alternatively you can try using path.contains , instead of path.Equals as this link suggests:
RewritePath[
^]
Hope this helps...Cheers.