The formalism of use here is not probability, but fuzzy sets. The Problem of the Heap basically highlights that "heapishness" is not a crisp property; there is not a clear-cut line between heaps and non-heaps, rather the demarcation between heaps and non-heaps is fuzzy. A collection of grains of rice can be more heapish or less heapish, and sufficiently non-heapish (for a given purpose, context, etc) collections can be called simply "non-heaps", of sufficiently heapish collections likewise simply called "heaps", but there is never a sudden switch from heap to non-heap.
Probability doesn't express that properly, because it still speaks as though a given collection either is or isn't a heap, and adds the further complication that two different collections of the same number of grains may be a heap and not a heap respectively, though their odds of being a heap are the same.
Going back to chickens: it's not that over time, successive organisms got more and more likely to be chickens. It's that over time, successive organisms got more and more chickenish. Chickens are not a crisp set. Chickenishness if a fuzzy property.
But stillsufficiently chickenish birds came before sufficiently-chickenish-bird eggs, because a chicken egg is an egg laid by a chicken, not necessarily an egg containing a chicken embryo. (Consider: when you buy unfertilized eggs at the store, are those chicken eggs or not?)