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();
   }                                           
 });