Fastest way to randomly shuffle an array based on probabilities in PHP?

I have an array with values and probabilities (or in PHP, keys and values):

Value   Probability
John    3
Peter   2
Paul    1

I want to shuffle this array but have the order be influenced by the probability. That is, on average John should appear at the top of the list half the time, Peter a third of the time, and Paul one sixth of the time. The average order over thousands of shuffles should be the one given above.

I have thought to

1. Create an array in which each value appears as often as indicated by the probability:

   John
   John
   John
   Peter
   Peter
   Paul
   

2. Shuffle this array, e.g.:

   John
   Paul
   Peter
   John
   John
   Peter
   

3. Remove the duplicates, leaving the first instance:

   John
   Paul
   Peter
   

In PHP code this might look something like this:

$items = array(
    'John' => 3,
    'Peter' => 2,
    'Paul' => 1
);

$probabilities = array();
foreach($items as $item => $value){
    $interim = array_fill(1, $value, $item);
    $probabilities = array_merge($probabilities, $interim);
}

shuffle($probabilities);

$result = array_unique($probabilities);

print("<pre>".print_r($result,true)."</pre>");

Is there a faster way to do this?

The real array contains a few hundred values and this probability-based shuffling has to be done everytime a webpage is called, so it should be lightning quick.