Suppose the number of dice you roll each turn of a game is either 1, 2, or 3. From one turn to the next, it changes from 1 to 2 with probability 0.67 (and stays at 1 otherwise). It changes from 2 to 3 with probability 0.21 (and stays at 2 otherwise). Finally, it changes from 3 back to 1 with probability 0.84 (and stays at 3 otherwise).

If on this turn the number is 1, what is the probability the number will be 3 on the third turn from now? Enter the exact probability in decimal form (no rounding).