Non-technical user here: why does Google make me use Captcha if it doesn't work? Error 503, etc. afterwards.
Probably a lot of users are trying to refresh calendar right now (which will probably hit the calendar service).
If they put ddos protection in front of it, it won't hit the calendar service but the ddos-protection-service.
My guess is that something bad has happened centrally, which tripped the security heuristics as an unexpected event at a very high level. It then elevated the security for a very large number of users.