I think you may have made a mistake. 9e-199 isn't the probability that no cock at all is being sucked at any given point in time, but rather that no cock is being sucked in a one minute interval during a given year, given that the year is broken into one-minute intervals and one blowjob is only considered to have occurred in one of these intervals. The consequence is that it's not fair to use a different interval for your moment. Probability doesn't exists in an "instant", but rather a probability density. In fact, using a smaller interval to estimate the probability of no cock being sucked at any given point of time would further justify your use of a Bernoulli process to model the probabilities when time is continuous, since the Poisson distribution is approximately equal to a Binomial distribution when the events are rare enough (i.e. have a negligible probability of occuring twice is the same interval, which is not the case when we look at minutes).

This changes the results significantly: There are 315567360 10-second moments in a year. Choosing one moment, it has a 6/315567360= 1.901e-8 probability of being a moment that a given cock is in a mouth (I think this is ok, although looking at more moments would cause the conditionals based on whether previously selected moments are part of a continuous 600-moment blowjob to become more complicated...). The probability that no cock at all is being sucked at a given moment is (1-1.9e-8)^2.4e8=1.0e-2. Given this probability per moment, and a 3.2e10 moment life, 1-(1-0.01)^3.2e10 gives me a probability of approximately 1, or rather, it almost certainly occurs that no dick is sucked at some point.

We could have more fun with a Poisson process explicitly, although it assumes that blowjobs occur independently of each other with a specific rate (and that they occur essentially instantly). Assume we blowjobs occur with an average rate of 2.4e8 blowjobs/year = 456.308 blowjobs/minute =0.76 blowjobs/moment. Then the probability that each positive number of blowjobs is occuring at a given moment is directly given by the Possion distribution with a lambda parameter of 0.7605, which is 0.467, a very possible number, while the possibility of no blowjobs in a minute is 6.73e-199, which is negligble and shows why you have to be careful about units.