http://mersennearies.sili.net/credit.php (put in a TF assignment and factoring range, as part of the result it says the chance of finding a factor)
That's the easiest way, since it applies the formula for you.
The actual formula is at:
http://www.mersenne.org/various/math.php
Quote:
the chance of finding a factor between 2^{X} and 2^{X+1} is about 1/x

Pretty simple.
But note that this only counts starting at about log_2(p) bits, since all factors must be of the form 2kp+1.
Whether there is a previously known factor does not make a difference in the distribution of further factors, but the TF depth does.