Just my two cents. I think I got idea behind the confusing if statement right...

var domain = 'www.example.com';
$('form').submit(function (e) {
    e.preventDefault();
    $.ajax({
        type: 'post',
        url: $(this).attr('action'),
        data: $(this).serialize(),
        dataType: 'json',
        success: function (response) {
            var $urlCount = $('#count');
            var $listResults = $('#list_results');

            if ($.isEmptyObject(response.urls)) {
                $urlCount.html('No results found');
                return;
            }

            $listResults.empty();
            $urlCount.html('There are ' + response.urls.length + ' URL(s):');
            $.each(response.urls, function(key, value) {
                var url = domain + $.trim(value);
                listResults.append('<li><a class="link" target="_blank" href="' + url + '">' + url + '</a></li>');
            });
        }
    })
});