I suspect the real question is something like how likely is it for 3 favourites in a row to win at a meeting.

By my calculations for an 8 race card, and a 30% chance of a favourite winning, the probability is 12%.

For true even money shots the chance is 42%.

This is not that hard to work out with a spreadsheet.

In the 1st case, 30% of your live samples are projected right, whereas 70% project back to square zero (aka column A).

Obviously the samples that make the run of 3 play no further part in the process.