if div has content show div

If you want to check for text, you can use the text() method:

 $(document).ready(function(){
   if ($("#box3").text().length > 0) {
     $('#third').show();
   }                                           
 });

Or for html:

 $(document).ready(function(){
   if ($("#box3").html().length > 0) {
     $('#third').show();
   }                                           
 });

For the updated question: Check the trimmed text of the inner <div>, like this:

 if ($.trim($("#box3 div").html())) {
   $('#third').show();
 }

Previous answer: If you want to show if it has anything, then checking :not() against :empty works:

 if ($("#box3:not(:empty)").length) {
   $('#third').show();
 }

If you want to check for any elements (not possibly whitespace only), then use :has(*), like this:

 if ($("#box3:has(*)").length) {
   $('#third').show();
 }

Related