User-agent: Googlebot
Disallow: /privatedir/
User-agent: *
Disallow: /
Now, what are disallowed for Googlebot: /privatedir/, or the whole website
According to the original robots.txt specification:
A bot must follow the first record that matches its user-agent name.
If such a record doesn’t exist, it must follow the record with User-agent: *
(this line may not appear in more than one record).
If such a record doesn’t exist, it doesn’t have to follow any record.
So a bot never follows more than one record.
For your example this means:
/privatedir/
.