Well, at one end of its spectrum of meanings, "probe" can mean "inspect with a physical probe", but as the meanings converge, I guess "probe" has more of a feel of an intensive, in-depth or systematic organised investigation, whereas "sound out" often means something like "ask/look around and see what you can find out", "have a chat with so-and-so and find out what he thinks", or something like that. In your example "sound out" seems to fit better. " Sentences begin with a capital letter.
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