Two parents can have a very large number of different potential offsprings, and it's common knowledge that the daughter chromosomes in meiosis are produced randomly, i.e. in crossover, the exact spots where the parent chromosomes are "cut" and genes are exchanged are random, with a larger probability at recombination hotspots.
I can't understand how the crossover process can just be completely random, what is exactly different in each trial that leads to different outcomes? Is there something at the molecular level that actually determines the outcome (e.g. the exact positioning and the orientation of the chromosomes or other cells/molecules involved in the process)?