What is the probability that a randomly chosen number from the set of c.e.numbers is period(number)?

What is the probability that a randomly chosen number from the set of computable numbers is period(number)?

For definition of period(number),please see www.maths.ed.ac.uk/~aar/papers/kontzagi.pdf.

Further more,if we replace period number with exponential periods,what are the probability in the question above?

The set of computable numbers includes set of periods or exponential periods ,what is the reverse?Is it true?or almost true in probability sense?