My short version of this problem is that we are dealing with one point statistics, in that we have one Universe, and the conditions are what they are. If you want to argue about how likely those conditions were before you knew about our Universe, the answer you get depends completely on the assumptions you make. In the language of Bayesian statistics, the answer is dominated by the prior (which is the probability you assume before you observe the data).
There is a similiar never ending bun fight in the literature around the probability of life forming. Some argue that the one data point we have (Earth) implies life will form very commonly in the Universe, some argue that the evidence of the timescales of evolution on Earth tell you it will be very rare. Others say that the one data point tells you very little. Again it all depends on the prior that is assumed (either implicitally or explicitally).
My own view is that the cosmological constant problem can't sensibly be answered using these kinds of arguements, and will require some other yet to be realised insight, which hopefully also points to new ways of verifying this new idea (e.g. predictions about experiments or observations that can be made but have not yet been done).
