JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/chosen/1.4.2/chosen.jquery.min.js"></script>
<select name="post_type" id="">
    <option value="selectone">select one</option>
    <option value="test">test</option>
    <option value="not-test">not-test</option>
</select>
<select name="second_dropdown" id="second_dropdown">
    <option value="cat1">Cat 1</option>
    <option value="cat2">Cat 2</option>
    <option value="cat3">Cat 3</option>
    <option value="cat4">Cat 4</option>
</select>

JavaScript

jQuery(document).ready(function ($) {
          var $secondDropdown = $('#second_dropdown'), $noOptions;

          $secondDropdown.append('<option id="no-options">Sorry, no options!</option>');
          $noOptions = $('#no-options').hide();

          $('select[name="post_type"]').change(function (event) {
              if ($('select[name="post_type"]').val() === 'test') {
                  $noOptions.prop('selected', true).show();
                  $secondDropdown.prop('disabled', true).trigger('chosen:updated');
              } else {
                  $noOptions.hide();
                  $secondDropdown.prop('disabled', false).trigger('chosen:updated');
              }
          });
      });