<image> The frequency distribution histogram of the scores ($$unit: points$$) of 20 students in a math test is shown in the figure:
$(1)$ Find the value of $$a$$ in the frequency distribution histogram;
$(2)$ Calculate the number of students whose scores fall within $$[50,60)$$ and $$[60,70)$$, respectively;
$(3)$ Randomly select $$2$$ students from those whose scores are within $$[50,70)$$, and find the probability that both students' scores are within $$[60,70)$$.