In the age of cloud, Grid, P2P, and volunteer distributed computing, large-scale systems with tens of thousands of unreliable hosts are increasingly common. Invariably, these systems are composed of heterogeneous hosts whose individual availability often exhibit different statistical properties (for example stationary versus non-stationary behaviour) and fit different models (for example Exponential, Weibull, or Pareto probability distributions). In this paper, we describe an effective method for discovering subsets of hosts whose availability have similar statistical properties and can be modelled with similar probability distributions. We apply this method with about 230,000 host availability traces obtained from a real large-scale Internet-distributed system, namely SETI@home. We find that about 34% of hosts exhibit availability that is a truly random process, and that these hosts can often be modelled accurately with a few distinct distributions from different families. We believe that this characterization is fundamental in the design of stochastic scheduling algorithms across large-scale systems where host availability is uncertain.