Simple Drupal hook_menu
Your URL is expecting an argument so your URL would have to be  http://mywebsite.com/example_callback/something. I wouldn't bother with the extra % in the path though.

So you should be doing something like and it will still pick up the arguments:

function example_module_menu() {
  $items = array();

  $items['example_callback'] = array(
    'title' =&gt; 'My Custom Callback',
    'page callback' =&gt; 'my_custom_php_function',
    'access callback' =&gt; TRUE,
    'type' =&gt; MENU_CALLBACK,
 );

 return $items;
}

/**
* Function that gets called from JQuery asynchronously. 
*/
function my_custom_php_function() {
  if (arg(1)) {
    // this means there is an argument
    // Do something with $argument...
  }
  return '';
}