Also, it is probably a good idea to find out why the message happened in the first place (don't just ignore it).
Did you enter your password wrong too many times on your phone?
Do you use the same password for multiple sites?
Is your friends getting SPAM from your Outlook account?
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how they could notice anything, are they spying on my messages?
what kinda of irregular activities? there's just emails in and emails out.
I wouldn't call it spying but monitoring your activity to try and help detect any thing out of the norm. It's more of a protection thing if anything. It's like when you make purchases with your bank debit card and when you make a sudden purchase over seas or the like they call just to verify.
I would update your password and scan all of your computers you've accessed your hotmail account from.