When will horses receive their post positions?

Horses receive their post positions from the random draw after the close of entries because this process ensures fairness and randomness in determining where each horse will start in a race. The post position can significantly impact a horse's performance, as it determines the horse's placement in relation to the starting gate and potentially influences the race dynamics. The random draw helps to minimize any biases that could arise from predetermined positions, allowing for an equitable chance for each entry in the race. Ensuring this draws confidence from trainers and owners that the process is impartial and conducted in the best interests of all competitors.

In this context, the other choices do not align with the established protocols of racing. Post positions are not assigned after the race is run, which would undermine the integrity of the race itself. They also aren't determined before races are drawn or upon arrival at the track, as this would negate the purpose of the entry process and the associated random draw.