MySQL 5.7

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CREATE TABLE table3
    (`id` int, `score` int)
;
    
INSERT INTO table3
    (`id`, `score`)
VALUES
    (1, 1),
    (2, 4),
    (3, 4),
    (4, 3),
    (5, 2),
    (6, 2),
    (7, 1),
    (8, 4),
    (9, 2),
    (10, 3)
;
SELECT `id`, `score`
FROM (SELECT `id`,`score`,if (id = 8,@scoreid:= @scoreid +1,@scoreid) scoreid  From table3, (SELECT @scoreid :=0) s  Order by score desc) t1 
Where scoreid > 0 LIMIT 3; 


id
score


8
4

4
3

10
3


SELECT `id`,`score`,if (id = 8,@scoreid:= @scoreid +1,@scoreid) scoreid, @rank := @rank + 1 as rank  From table3, (SELECT @rank:=0) r, (SELECT @scoreid :=0) s  Order by score desc


id
score
scoreid
rank


2
4
0
1

3
4
0
2

8
4
1
3

4
3
1
4

10
3
1
5

5
2
1
6

6
2
1
7

9
2
1
8

1
1
1
9

7
1
1
10