Is there a language with constrainable types?

Question

Is there a typed programming language where I can constrain types like the following two examples?

1. A Probability is a floating point number with minimum val

Answer 1

Modula 3 has subrange types. (Subranges of ordinals.) So for your Example 1, if you're willing to map probability to an integer range of some precision, you could use this:

TYPE PROBABILITY = [0..100]

Add significant digits as necessary.

Ref: More about subrange ordinals here.