Keep $(".thumbList").selectable();
in a separate function in main page.
function iniThumbList(){
$(".thumbList").selectable( /* wt ever the your remaining code */);
}
After document initialization call iniThumbList(); This is the initial behavior of your code. Now After the ajax completion when you have new content inside the DOM call iniThumbList(); This way you don't have to repeat the code and it's easy to read it even at a later time.
$.ajax({
url: "test.html"
})
.done(function( html ) {
$( "#results" ).append( html );
iniThumbList();
});