Often one is using this principle when, upon coming to a conclusion, begin with the phrase "surprise, surprise, it turns out that..."
More often than not this principle is a very good starting point for prove things. Since you would be very surprised if it turned out to be incorrect, you already have a goal in mind. Sometimes actually proving that the assumption is true can be much more difficult.
Take, for example, the Fermat's Last Theorem[2]
xn + yn=zn
has no non-zero solutions for n > 2.
What's is wholely remarkable about this particular theorem is that it would have been incredibly surprising to find that it was false. But finding a correct proof of this theorem took centuries and the cumulative work of many mathematicians.
There is another application of the Principle, which lies in the software space. When there is ambiguity, the software should do the least surprising of the two actions. An example of the opposite of this is an instance where a dialog pop-up appears asking the user whether or not they're really, absolutely sure they want to do that. The user is given the option of yes, no or cancel. Clicking cancel exits the application.
Very surprising.
It's point in UI design is intended to guide a developer to make interfaces that are moderately intuitive. Given it's other name, it certainly sounds like it has very boring outcomes. However it's a good road to happy customers, which means the software producer will never be bored, racing down the highway in his fancy, expensive sports car.
[1] Absolute Astronomy Reference
[2] Fermat's Last Theorem
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