Forbid contributors viewing drafts

Is there any way I can forbid a contributor to view draft posts? Right now any contributor can view my draft posts and even edit them (however their edits must be approved by administrator first).

Yes, but you might need a plugin like ‘User Role Editor’. You can then edit the capabilities of roles, including contributors.

So they can edit their own posts/drafts, but not the posts/drafts of others you should ensure that core capabilities:

• edit_posts is checked.
• edit_others_posts is unchecked