Postgres 13

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

create table table1(Col1 int,	Col2	int,Col3 int);
insert into table1 values(100	,200	,1);
insert into table1 values(100	,201	,1);
insert into table1 values(100	,202	,1);
insert into table1 values(100	,203	,1);
insert into table1 values(101	,204	,1);
insert into table1 values(101	,205	,1);
insert into table1 values(102	,206	,1);

CREATE TABLE

INSERT 0 1

INSERT 0 1

INSERT 0 1

INSERT 0 1

INSERT 0 1

INSERT 0 1

INSERT 0 1

with cte as(
   select col1,col2,col3, row_number()over (partition by col1 order by col2) rn from table1
)
update table1 set col3=cte.rn
from cte
where table1.col1=cte.col1 and table1.col2=cte.col2;

UPDATE 7

select * from table1;

col1
col2
col3

100
200
1

100
201
2

100
202
3

100
203
4

101
204
1

101
205
2

102
206
1

SELECT 7