How do I make the page created from my module visible only to anonymous users? I programatically created a page using the following code.

/**
* Implements hook_menu().
*/
 function page_prog_menu() {
   $items['page_prog/custom'] = array(
     'title' =&gt; 'My Custom page',
     'page callback' =&gt; 'page_prog_custom',
     'access arguments' =&gt; array('access content'),
   );
   return $items;
 }

 /**
 * Custom callback function.
 */ 
 function page_prog_custom() {
   $content['raw_markup'] = array(
     '#type' =&gt; 'markup',
     '#markup' =&gt; '&lt;p&gt;Hello world&lt;/p&gt;',
   );

 return $content;
 }


I need to make this page visible only to anonymous users. How can I achieve this? 

I have tried with hook_permission(), but it doesn't help.

/**
* Implements hook_permission().
*/
function page_prog_permission() {
  return array(
    'access page_prog content' =&gt; array(
    'title' =&gt; t('Access content for the pages created programatically'),
    )
  );
}
'access arguments' => array('access page_prog content'),