SQL Server :: Update Multiple Row With Different Value?

The goal is to update multiple row in the table. In my table there is 3 col, at here i will name it col1, col2 and col 3. The number of row in the table is, let say 10. Each row will have a different value in col1 and col2, where col3 value is static.

Something like the below;
|col1 |col2 |col3
Row1 |a |b |c
Row2 |aa |bb |c
Row3 |aaa |bb |c

My update statement;

UPDATE table1 SET Col2 = CASE Col1
WHEN 'a' THEN '1'
WHEN'aa' THEN '2'
End where col3 IN (c)

In plain, i just wanna update col2, but had to base on col1 and col3 value. After I run the statement above, it will empty Row3's col2, but in fact, i don't want to update Row3's col2.