How to work with array_map

foreach is going to be simpler than array_map() here. I also make use of array_key_exists() and ksort() to make things cleaner. See my documented example below.

Example:

// Data.
$initialArray = array(
    'Anto' => 25,
    'Filip' => 22,
    'Marko' => 17,
    'Josip' => 23,
    'Igor' => 24,
    'Ivan' => 23,
);
$newArray = array();

// Loop.
foreach($initialArray as $name => $age) {
    if(!array_key_exists($age, $newArray)) {
        // Initialize this age in the new array with empty counter.
        $newArray[$age] = array(0);
    }

    // Increment the counter.
    $newArray[$age][0]++;

    // Append the name.
    $newArray[$age][] = $name;
}

// Sort by age.
ksort($newArray);

// Dump.
print_r($newArray);

Output:

Array
(
    [17] => Array
        (
            [0] => 1
            [1] => Marko
        )

    [22] => Array
        (
            [0] => 1
            [1] => Filip
        )

    [23] => Array
        (
            [0] => 2
            [1] => Josip
            [2] => Ivan
        )

    [24] => Array
        (
            [0] => 1
            [1] => Igor
        )

    [25] => Array
        (
            [0] => 1
            [1] => Anto
        )

)

This is just one of many ways to do this. I strongly suggest reading more into the foreach control structure so that you grasp the concept fully...it'll be necessary moving forward as a programmer!

You could also do this by adding the counter at the end of your logic. First, you would go through and sort each name into an array based on their age. Then, you would go through and prepend the count($names) to the beginning of the $names array at $age index.

You can use array_walk for this. Here you go:

$array = [
    'John' => 25,
    'Tony' => 25,
    'Anto' => 25,
    'Filip' => 22,
    'Marko' => 17,
    'Josip' => 23,
    'Igor' => 24,
    'Ivan' => 23,
];

$ages = [];

array_walk($array, function ($age, $name) use (&$ages) {
    // Does the age already exist? If so, we'll increment
    // the count, otherwise we'll initialize it to one.
    array_key_exists($age, $ages) ? $ages[$age][0]++ : $ages[$age][0] = 1;

    $ages[$age][] = $name;
});

var_dump($ages);

Output:

array:5 [▼
  25 => array:4 [▼
    0 => 3
    1 => "John"
    2 => "Tony"
    3 => "Anto"
  ]
  22 => array:2 [▼
    0 => 1
    1 => "Filip"
  ]
  17 => array:2 [▼
    0 => 1
    1 => "Marko"
  ]
  23 => array:3 [▼
    0 => 2
    1 => "Josip"
    2 => "Ivan"
  ]
  24 => array:2 [▼
    0 => 1
    1 => "Igor"
  ]
]