It depends on the definition of the term postcondition. In general, a precondition is a relation on input state and input values at routine entry, and a postcondition is a relation on input state, input values and output state and output values at routine exit.
Because a routine can exit either normally or exceptionally, it is possible to define a postcondition for normal termination and a postcondition for abnormal termination. Clearly both involve input values, input state and output state. The key difference is in output values. In the first case this is a value specified in the routine signature, in the second - it depends on the language. In your example it might be NoPathException, but what if there is a memory allocation error, stack overflow or other exception or signal that is not specified in the signature? It may indeed seem to be possible to have a precondition that guarantees that there is always a valid result that does not involve exceptions. But this is not the case, e.g. when there is communication to external world, concurrency, etc. Also if a precondition is too costly to compute, it does not look nice to do the same work twice - on the client side to make sure a call is applicable and on the supplier's side to do essentially the same computation to get the result.
According to the Design by Contract philosophy a postcondition is what the client can safely rely on after calling a routine. Coming back to the exceptional case, from the practical point of view it makes sense to make the abnormal postcondition strong enough so that a program can continue execution, but weak enough so that the cases that are not or cannot be specified in the signature, but are possible in practice, are allowed.
So, unless the language does really guarantee all possible exceptional cases and nothing else, the most important part is output state that should not make the associated objects unusable. And this could either be expressed in an explicit or implicit postcondition or as a class invariant.
As to the specific example with getPath, the situation when a path does not exist is normal, i.e. it may happen, is expected. Some guidelines recommend to use normal values to indicate normal termination cases. Here it would be value null. Using null may lead to other issues on the caller's side, such as NullPointerException if result is not checked for null-ness, but in some languages that guarantee absence of such exceptions (e.g., void-safety in Eiffel) this would be the preferred way to indicate absence of a path (the return type would be detachable PATH in that case).
