JQuery :: Function Runs Before HTML Updated By Ajax

Problem in the timing of the script. The problem is that when I try to get an id of an object that was added by ajax, the script doesn't recognize it. The html:
<select id="categories" name="categories">
<option value="3">aa</option>
<option value="43">bbb</option>
</select>

When I load the page, there is this script that get the value of the #categories and use ajax to fill another select and in the same ajax, I load images by another function using the new select input that was created:
function fill_subcategories(){
parent=$("#categories").val();
$.ajax({
type: "post",
url: "ajax/sub_galleries.php",
data: 'parent='+parent,
success: function(data){
$('#sub_categories').html(data);
}});
show_exist_imgs()
}

This fills this div:
<select name="sub_categories" id="sub_categories"></select>
Right after filling the #sub_categories, I use another ajax that get images of the new id of the #sub_categories, and here I get the problem.. the js:
function show_exist_imgs(){
g_id=$('#sub_categories').val();
$.ajax({
type: "post",
url: "ajax/show_exist_imgs.php",
data: 'g_id='+g_id,
success: function(data){
$('#exist_files').html(data);
}});
}
This script doesn't recognize the id of the new $('#sub_categories') select input.. why is that?