The answer can be approximated as 1/(5000*sqrt(2*π)) =~ 0.000797885 =~ 1 in 1253.314137.
Recall the equation for the standard normal curve:
The expected number of tails in one flip is 0.5 and the expected squared number of tails is also 0.5. Thus, the variance of the number of tails in one flip is 0.5-(0.5)2 = 0.5 - 0.25 = 0.25. The variance of one million flips is 1,000,000 * 0.25 = 250,000. The standard deviation of one million flips is the square root of that: sqrt(250,000) = 5,000.
Let x = the number of tails over the expected number of 500,000. The mean of x is zero. As shown, the standard deviation of x is 5,000.
The probability of x=0 is thus:
This simplifies to 1/(5000*sqrt(2*π)) =~ 0.000797885 =~ 1 in 1253.314137.
Links
Wikipedia entry on the standard normal curve.