I happened to stumble across a private profile on Bitbucket, and this was what I saw:

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-vgnR5g8gcxbfAyiTUZwodNSUFhvLDtU3O3nlkxF1-f2rC2erC3tzK-nhnc5NwSlZg39c0W4eQ8c5eMrGhmbLWXK3w37xf7Q_6Dezktbgx0O9-iowe34jN462jEEyqSoV0GGjG6ejeZk/s800-Ic42/2015-07-18--06%25253A42%25253A44.png

You were never here

This user has requested we keep their identity a mystery. Let’s never speak of this again.

I thought this is humorous, like Chrome’s Incognito Mode, and believed this was my first time accessing a private profile page, but it’s not. The first time was almost two years ago, Bitbucket changed it a bit, more seamless.

As for its 404 page, it hasn’t been any changes in more than two years

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdiSs92aoBYy59qjcuIpR898PYS6tyGrvWANxz7bZ0tYdkfLa6IG6xcjBPVCRaaLqSnJDfYxufK4YKgOnXTfhFxHteRMPlyefQ6V_6uqMJx84D1nk1qb08osSsedKLGYb9Kk0R42VNFpA/s800-Ic42/2015-07-18--06%25253A42%25253A51.png

Bitbucket allows unlimited private repositories for no charges, it makes sense to allow Private Profile, but

let’s never speak of this again.

And you have never seen this page.