If you are looking for a way to view a private profile then you should navigate to How To View Privat Facebook Profiles.
Here I will explain how to view profile picture in a bigger size instead of the small icon.
Follow this steps to see the private facebook profile page picture:
1. Navigate to the private profile
2. Right click on the small profile picture
3. Copy and paste the picture link to the browsers address bar
4. Change the s to n in the link like this:
http://profile.ak.facebook.com/profile6/5/67/s534692250_9296.jpg
to
http://profile.ak.facebook.com/profile6/5/67/n534692250_9296.jpg
5. Press Enter
*Note* latest facebook version allows you to see the normal size picture without any access to the profile. However there are still cases when you are only able to see the small version of the profile picture and this trick will be useful