Why Ajax Doesn’t Work?

You should move this code into a new plugin instead, e.g. save this file as wp-content/plugins/example-ajax-handler.php

<?php
/*
Plugin Name: Example AJAX handler
Description: Handle example_ajax_request admin-ajax requests
Version: 0.0.1
*/

add_action( 'wp_ajax_example_ajax_request', 'example_ajax_request' );
add_action( 'wp_ajax_nopriv_example_ajax_request', 'example_ajax_request' );

function example_ajax_request() {
  if ( isset( $_REQUEST ) ) {
    $postID = $_REQUEST['postID'];
    print $postID;
  }
  wp_die();
}

then you’ll need to activate it from your admin site’s plugin menu. Then it should work! See the Plugin Basics documentation.