On a table are given $1999$ red candies and $6661$ yellow candies. The candies are indistinguishable due to the same packing. A gourmet applies the following procedure as long as it is possible: (i) He picks any of the remaining candies, notes its color, eats it and goes to (ii). (ii) He picks any of the remaining candies, and notes its color: if it is the same as the color of the last eaten candy, eats it and goes to (ii); otherwise returns it upon repacking and goes to (i). Prove that all the candies will be eaten and find the probability that the last eaten candy will be red.