If using XFBML, than you should wrap your like button code, eg.
into a div or span, eg:
Than, after gaining new URL via ajax, you have to clear already generated facebook like widget, and replace it with new fb:like code
jQuery('.fb-like').html('');
And than you have to initialize facebook like button again
FB.XFBML.parse();
Final code could looks like this one. Assume that response contains pure new URL
Summary:
To refresh facebook like button (or any other facebook XFBML) you have to:
1) destroy existing initialized widget (clear the content of XFBML code wrapper)
2) add new XFBML code into wrapper
3) initialize new code via FB.XFBML.parse();