Disable directory listings with 404 instead of 403
Enable mod_rewrite and AllowOverride in /secret. Then create .htaccess:
RewriteEngine On RewriteBase /secret RewriteRule ^$ - [R=404,L]
I've looked around the internet for an answer to a similar problem. While mod_rewrite is a possible solution, I find the best solution uses the "RedirectMatch" directive.
See StackOverflow: Problem redirecting 403 Forbidden to 404 Not Found