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This should do:

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort($sticky);
$sticky = array_slice($sticky, 0, 3);

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value === $GLOBALS['post']->ID)
        // ... and remove
        unset($sticky[$key]);

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

// EDIT
If you want to have 3 posts (no matter what), you have to do it like so (minimally changed):

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort($sticky);

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value === $GLOBALS['post']->ID)
        // ... and remove
        unset($sticky[$key]);

$sticky = array_slice($sticky, 0, 3);

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

This should do:

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort($sticky);
$sticky = array_slice($sticky, 0, 3);

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value === $GLOBALS['post']->ID) {
        // ... and remove
        unset($sticky[$key]);
        break;
    }

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

If you want to have 3 posts (no matter what), you have to do it like so (minimally changed):

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort($sticky);

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value === $GLOBALS['post']->ID) {
        // ... and remove
        unset($sticky[$key]);
        break;
    }

$sticky = array_slice($sticky, 0, 3);

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

// EDIT: added break after current post ID has been found and removed, in case you have a great number of sticky posts.

This should do:

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort( $sticky );
$sticky = array_slice($sticky, 0, 3);

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value->ID === $GLOBALS['post']->ID)
        // ... and remove
        unset($sticky[$key]);

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

// EDIT
If you want to have 3 posts (no matter what), you have to do it like so (minimally changed):

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort( $sticky );

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value->ID === $GLOBALS['post']->ID)
        // ... and remove
        unset($sticky[$key]);

$sticky = array_slice($sticky, 0, 3);

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

// EDIT: now accessing global post object.

This should do:

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort($sticky);
$sticky = array_slice($sticky, 0, 3);

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value === $GLOBALS['post']->ID)
        // ... and remove
        unset($sticky[$key]);

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

// EDIT
If you want to have 3 posts (no matter what), you have to do it like so (minimally changed):

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort($sticky);

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value === $GLOBALS['post']->ID)
        // ... and remove
        unset($sticky[$key]);

$sticky = array_slice($sticky, 0, 3);

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

This should do:

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort( $sticky );
$sticky = array_slice($sticky, 0, 3);

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value->ID === $post->ID)
        // ... and remove
        unset($sticky[$key]);

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

// EDIT
If you want to have 3 posts (no matter what), you have to do it like so (minimally changed):

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort( $sticky );

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value->ID === $post->ID)
        // ... and remove
        unset($sticky[$key]);

$sticky = array_slice($sticky, 0, 3);

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

This should do:

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort( $sticky );
$sticky = array_slice($sticky, 0, 3);

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value->ID === $GLOBALS['post']->ID)
        // ... and remove
        unset($sticky[$key]);

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

// EDIT
If you want to have 3 posts (no matter what), you have to do it like so (minimally changed):

// Get sticky posts
$sticky = get_option('sticky_posts');
rsort( $sticky );

// Check if current post is inside
foreach ($sticky as $key => $value)
    if ($value->ID === $GLOBALS['post']->ID)
        // ... and remove
        unset($sticky[$key]);

$sticky = array_slice($sticky, 0, 3);

$query = new WP_Query(
    array(
        'post__in' => $sticky,
        'ignore_sticky_posts' => 1,
    )
);

// EDIT: now accessing global post object.