Dale,

The bookie place price would be 1/5 for a $4.20. So to work this out you do the following ($4.20-1)/5+$1.00 = $1.64

Of course this isn't the best way to estimate the palce price but its the approximation. If you were to do the Harville method you would assume it had the following (assuming 3 place prices).

It has a 23.8% chance of coming first. If you know the rest of the horse prices you could then work oiut its chance of runing second. I'll assume 8 other horses all priced at $10 which is a 93% bookie market. So if a horse at $10 ran first the horse has a chance of 26.45% of running second. If a $10 horse runs second it has a 29.7% chance of running third. Add all these up and it has a 50.50% chance of running a place. Based on this the price should be $2.00

I hope that makes sense.