It is true that prob of fixation is the frequency at any given time. This can be seen with coalescence diagrams too.
Allele fixation is independent of previous history.
Coalescence theory says that all alleles present in a population share a common ancestor some time in history. Which means that the allele that was present at that time has become fixed. Hope that helps some. If not, let me know. It is true that prob of fixation is the frequency at any given time.