How can I be sure that no one consults the information in my vault?

Your vault is locked and stored on protected servers. Only you and the contacts to whom you have granted access (sharing feature) may access your documents.

Access to your account and document handling are recorded using the History function.

After your death, depending on your decision as to what will become of them, the contents of your vault will be destroyed, either directly (option 2&3), or after having been transferred to heirs (option 1) (see question What becomes of my vault and its contents after my death?)