For both discrete and continuous time probabilities, the existence of a set containing infinite possible values or outcomes is always implied as a theoretical limit that consistently obeys the laws of large numbers (weak and strong).
In the 1-dimensional real timeline, the probability density function (pdf) is given by
negative values represent time past. Positives are for time future, and time zero indicates the present state of now. For absolute Newtonian system, the zero time position is fixed, but for relative Einsteinian, the zeros positions change according to the movements of inertial frames, which indicate proper time of relative rest and absolute simultaneity.
The shiftings of relative time zeros indicate sharing of one single 'zero' for different ages of people alive here and now. Relative to this 'zero' the deads are located at all negative infinity time points to the left of zero and the future of unborns are in the positive values of the timeline toward positive infinity. All the deads have crossed Thom's fold catastrophe, while the livings are inevitably moving toward the edge of the fold.