Use AJAX to modify $wpdb query

Hello,

I work on a website where I display a list with a custom database table :

$resultats = $wpdb->get_results(
   $wpdb->prepare( "SELECT * FROM {$wpdb->prefix}prfs" )
   );

foreach ( $resultats as $resultatProfs ) { }

I try to create an AJAX filter with select input. I tried since yesterday but I don’t understand how to make this.

My functions.php :

function blog_scripts() {
    // Register the script
    wp_register_script( 'custom-script', get_stylesheet_directory_uri(). '/js/ajax.js', array('jquery'), false, true );

    // Localize the script with new data
    $script_data_array = array(
        'ajaxurl' => admin_url( 'admin-ajax.php' ),
    );
    wp_localize_script( 'custom-script', 'blog', $script_data_array );

    // Enqueued script with localized data.
    wp_enqueue_script( 'custom-script' );
}
add_action( 'wp_enqueue_scripts', 'blog_scripts' );

add_action('wp_ajax_get_states_by_ajax', 'get_states_by_ajax_callback');
add_action('wp_ajax_nopriv_get_states_by_ajax', 'get_states_by_ajax_callback');

My AJAX :

jQuery(function($) {
    $('#departement_select').change(function () {
        var departement = $(this).val();
        console.log(departement);
        if(departement != '') {
            var data = {
                'action': 'get_states_by_ajax',
                'departementValue': departement,
                'security': blog.security
            };

            $.post(blog.ajaxurl, data, function(response) {
                $('.load-state').html(departement);
            });
        }
    });
});

My php page :

<div class="load-state"></div>

<?php function get_states_by_ajax_callback() {
    check_ajax_referer('load_states', 'security');
    $departement = $_POST['departementValue'];
    var_dump($departement);
    global $wpdb;
    $aStates = $wpdb->get_results( $wpdb->prepare( "SELECT nom FROM ". $wpdb->prefix ."profs WHERE departement_fr = %d", $departement ) );
    if ( $aStates ) {
        echo('yep');
    } else{
        echo('nope');}
    wp_die();
} ?>