Birthdays won't show up in calendar [not using iCloud]

Hi all,

I just missed a birthday of a good friend and realized my iPhone didn't notify me. I checked my calendar and there was no entry.

I have to admit that I am not using iCloud calendar. I am using my Hotmail account (e-mail & calendar). The reason is simple. iCloud software doesn't run well on my Windows PC and it doesn't sync correctly. But this is another issue I don't want to discuss.

But: most of the contacts are saved using iCloud, but I am not using iCloud for the calendar. In each contact there is a birthday, but it doesn't show up in my calendar. Even it doesn't show up in my Hotmail Calendar.

When opening the calendar app and clicking the calendar option below in the middle it shows me this (its in German. Geburtstage means Birthdays):

And this is my standard calendar (in settings). I am using Hotmail because in Outlook on my PC I am using Exchange Mail Calendar and it syncs better than iCloud.

But I want the birthdays. Anyone have any idea? If I can't find a solution I may completely switch to Hotmail/Outlook 365 for syncing all of my contacts and calendar or in worst case, to Google.

Thanks

ps.: iPhone 7 Plus and newest iOS