I think only MX records indicate any priority for each additional record returned, for A records theres no indication of which records have priority over others and the usual behavior of authoritative DNS servers is to rotate the order in which records for the same thing are returned, so effectively returning more than one record for the same question results in a distribution of requests to the IPs returned rather than any sort of failover behavior.

In the case of the software Microsoft uses, it monitors endpoints for the websites in question and then changes which IP(s) are returned based on the availability of those endpoints, the geographic region and other factors.