hotmail.com is nowadays just one of several aliases for outlook.live.com, so that's where you'd expect to end up. Just sign in with your Hotmail email address and password when you get there. Noel Burgess MVP (Ret'd)
If you use Outlook.com to access an account that uses a domain other than @live.com, @hotmail.com, or @outlook.com, you might not be able to sync your accounts using IMAP. To resolve this, remove the connected IMAP account in Outlook.com and reconfigure it as a POP connection.