Coin Race #2

You keep flipping a coin, and while you do this, you keep track of the number of Heads and the number of Tails. You can think of this as a race between Heads and Tails. For example, if after 8 flips you have landed on Heads 6 times and Tails 2 times, then Heads is winning the race by 4. Now consider a race of 10 flips. If you flip Tails first, what is the probability that Heads will be winning the race?

Answer format: round to 3 decimal places.