What is the probability of living now? The philosophical problem here, is that there is no definite meaning of 'living at a particular date', and we get very different answers to our question depending on whether we are referring to phenomenal aspects of time comprehension, mathematical descriptions of time, or public denotations of time as a network of synchronized clocks and calendars. These relations are very complex, and our theoretical definitions are under-determined.
If we think of time in the traditional realist way, we think of nature as the real calendar of events that we culturally represent and approximate using our calendars; we naturally end up interpreting existential probabilities across time in terms of a linear scatter-plot of calendar-ordered frequencies. Consequently we end up with a philosophically dissatisfying answer to our philosophical question as to the probability of living at a particular time, for all we end up here is with a circular framing of the problem that answers in terms of frequencies, when we were implicitly questioning the relationship between calendar use, physical time, and personal experience.
On the other hand, when trying to understand time directly in terms of personal experience, we run into the problem that the content of personal experience is vague and repeatable without an absolute ordering; I cannot, for instance, distinguish the current appearance of my living room wall from its appearance last Wednesday. So my living room wall does not serve as a calendar.
I am only able to refer to the appearances of my living room wall at different dates by taking it's appearance in conjunction with something else serving as a calendar - for example, other memories I have that are different from one another and that I associate individually with the respective dates. Or if my memory is failing, photographs. But then a similar problem of repeatability resurfaces with respect to the conjunctions of experiences; we can therefore only speak of calendar-like relations as existing between phenomena when they are suitably interpreted, but we cannot phenomenally speak of the existence of absolute calendars - in direct contradiction to realist intuitions.
Phenomenal time therefore isn't linearly ordered and non-repeating as suggested by calendars; and the psychological past isn't immutable and separable from the psychological future, rather they are both mutable and inseparable aspects of present experience. Therefore any empirical attempt to conceptually reduce physical time to a phenomenal foundation must abandon the linear-ordered-time orthodoxy; Cartesian notions of time are merely practically convenient, without a phenomenally legible basis.
On the surface, the law of entropy sound appealing as a justification for absolute temporal ordering. However, entropy cannot serve as a justification for an absolute temporal order; for the notion of increasing disorder is relative to the labeling conventions we use for describing a system, and in science our labeling conventions are deliberately chosen so as to maximise the information we get from an experiment. Entropy is therefore an epistemological notion as opposed to a physical or metaphysical notion. From an omniscient perspective, there is no absolute 'law' of entropy.
The assumption of time symmetric microscopic laws is a big give-away that entropy isn't real; for any microscopically time-symmetric system that is observed to decrease in order, there exists an alternative labeling of it's micro-states in which it is described as increasing in order; to see this, simply imagine a simulation of a deck of cards being shuffled. At the end of the simulation, identify the top three cards on the shuffled stack and give them an identical label. Then replay exactly the same simulation from the beginning, remembering the cards we previously labelled. When re-interpreted with respect to this new labeling convention, the card shuffle increases in order. Therefore entropy isn't a phenomenal intuition and neither is it a physical concept. Entropy refers purely to epistemological uncertainty; to state it mathematically: Given a random assignment of labels to micro-states, the average entropy change of a time-symmetric system is zero.