Some of Adobe's subscription services for creative professionals currently are hosted on Amazon's AWS. It's not clear from Microsoft's announcement of its new Adobe deal whether Adobe's Creative Cloud, Marketing Cloud, and Document Cloud will run on any other cloud backbones, with Azure as a secondary option or choice. I've asked Microsoft, and heard back from a spokesperson that today's deal is not exclusive, but that's all I know at this point.
Work is underway to move these services to the Azure cloud, a spokesperson confirmed, with more information on this coming in the next few months.
Update: An Amazon spokesperson shared the following statement about what the Azure deal doesn/doesn't mean for Adobe and Amazon:
"We have a significant, long-term relationship and agreement with Adobe that hasn't changed. Their customers will want to use AWS, and they're committed to continuing to make that easy."
The press release announcing the Microsoft-Adobe partnership today doesn't mention AWS at all. It says "Adobe will make Microsoft Azure its preferred cloud platform" for the above-mentioned services. The release mentions that Adobe also will get access to the machine learning, cognitive services like the Cortana Intelligence Suite and SQL Server.
For its part, Microsoft will make the Adobe Marketing Cloud its "preferred marketing service" for the coming Dynamics 365 Enterprise Edition, which is expected to be available in 2017. This combined offering is part of Microsoft's play to provide more intelligent sales and marketing services to compete with Salesforce, Oracle, and others in this space who are also touting their artificial intelligence prowess.