Neil has it right -- there's no true way to measure how many amps are left in a battery. You can get an indication of what is likely to remain by measuring the voltage, but since that doesn't decrease linearly as the battery discharges - it'll only give you a rough indication of remaining charge.
I do not know how "remaining battery charge" is measured in things like our laptop. It's got a small icon that show percent of remaining charge. I've never tried to figure out if it is accurate. And even if it is -- the battery in the computer is probably way different than one in your race vehicle, so it wouldn't necessarily give comparable results.
You could come up with some kind of a good number, though, by measuring two things separately and using some math to get your figure for remaining capacity. First - measure the current draw while operating, and second, measure how long it's drawing that amount. If the engine has an electric starter it'll draw quite a big amount for the seconds that the starter is running (maybe 10 seconds? Maybe 4 tries at 15 seconds each? Whatever. . .). And the amount the engine draws while running will likely be a relatively small amount for a longer time (3 minutes or so for a bit of warmup and a 3-mile run down the short course plus a bit of time for your turn-out.
I have plugged in some W A Guesstimate numbers. Yours may be wildly different.
Battery states 300 amp-hour reserve.
20 seconds of 100 amp* draw = .55 amp hours
4 minutes of 10 amp* draw = 6.66 amp-hours
Result: You've used about 6 1/4 amp-hours, or about 1/16 of your battery's stated reserve. Allowing for dropping voltage as the 100 amp hours is/are used up -- I'd hazard to guess that instead of the implied 16 start/run events -- you might get eight of 'em before the battery is too tapped-out to crank the engine.
In other words, it ain't gonna be easy to figure out how much you've got remaining -- no matter how you do it. Best of luck. C U at WoS.