How to fetch a not so random value from an array?

The idea

At work, we've got a task no one wants to do. So I tried making a script that randomly selects a person from an array and displays their name. However, when we have an intern, we want him/her to turn up more often than the others.

Keep in mind this is just some fooling around with code.

Code

<?php
if (!isset($_COOKIE['names'])) {
    // Prepare initial array
    $names = array(
        'John Doe' => 10,
        'Jane Doe' => 10,
        'Mike Doe' => 10,
        'Gina Doe' => 10,
        'Anne Doe' => 10,
        'George Doe' => 10,
        'Jack Doe' => 10,
    );

    // Create cookie
    setcookie('names', serialize($names), time()+28800);
}

$names = unserialize($_COOKIE['names']);

$randomArray = array();
foreach ($names as $name => $probability) {
    if ($probability > 1) {
        foreach (range(1, $probability) as $v) {
            $randomArray[] = $name;
        }
    } else {
        $names[$name] = 10;
    }
}

$selected = $randomArray[array_rand($randomArray)];
if (array_key_exists($selected, $names)) {
    if ($names[$selected] > 1) {
        $names[$selected]--;
    }
    setcookie('names', serialize($names), time()+28800);
    echo $selected;
}

By looking at this code, I guess you'll get the general idea. By making the probability higher, people's name will come up more often.

The problem

When the probability comes to 1, I set it back to 10. But somehow this feels wrong. I am not a calculus miracle but my head can figure out that this just isn't right. Also, the piece of code I wrote doesn't feel efficient at all. In my opinion there are too many loops.

What I wold like to ask is for you to take a look at my code and tell me what it is I'm doing wrong and what I can do to improve it. Suggestions etc. are also welcome.