I think this should work... I wasn't able to test on your example array but it seems to work on a smaller array I made.
Edit: Changed the function now that you've removed the 'depth' keys from your example array. Now it finds the depth on its own. I've also added my test code and output:
<?php
function array_depth_count(&$array, $count=array(), $depth=1) {
    foreach ($array as &$value) {
        if (is_array($value)) {
            $value['count'] = ++$count[$depth];
            array_depth_count($value, $count, $depth + 1);
        }
    }
}
$a = array(array(array(array(0),array(0),array(),array()),0,array()));
echo "Before\n";
print_r($a);
array_depth_count($a);
echo "\n\nAfter\n";
print_r($a);
?>
Output:
Before
Array
(
    [0] => Array
        (
            [0] => Array
                (
                    [0] => Array
                        (
                            [0] => 0
                        )
                    [1] => Array
                        (
                            [0] => 0
                        )
                    [2] => Array
                        (
                        )
                    [3] => Array
                        (
                        )
                )
            [1] => 0
            [2] => Array
                (
                )
        )
)
After
Array
(
    [0] => Array
        (
            [0] => Array
                (
                    [0] => Array
                        (
                            [0] => 0
                            [count] => 1
                        )
                    [1] => Array
                        (
                            [0] => 0
                            [count] => 2
                        )
                    [2] => Array
                        (
                            [count] => 3
                        )
                    [3] => Array
                        (
                            [count] => 4
                        )
                    [count] => 1
                )
            [1] => 0
            [2] => Array
                (
                    [count] => 2
                )
            [count] => 1
        )
)
                  yjerem
                   2009-02-07 08:23:51