sqlite correct path/URI for php pdo on windows

[ante-scriptum : this is a self answered question, you don't need to bother answering]

I ran into a weird configuration problem, not documented anywhere on the specific PHP.net page or at StackOverflow.

The problem

When opening an existing sqlite database on Windows, the same error kept showing :

SQLSTATE[HY000] [14] Unable To Open Database File

Although the code executed was copy/pasted from the manual :

<?php
/* Connect to an ODBC database using driver invocation */
$dsn = 'sqlite:/full/path/to/db';
$user = 'dbuser';
$password = 'dbpass';

try {
    $dbh = new PDO($dsn, $user, $password);
} catch (PDOException $e) {
    echo 'Connection failed: ' . $e->getMessage();
}

?>

I could not open this database, as I had tried all kinds of various DSN while googling :

$dsn = 'sqlite:/c:\\full\\path\\to\\db'; // --FAILED--

$dsn = 'sqlite://c:/full/path/to/db'; // --FAILED--