What is the justified true belief account of knowledge and what is Gettier's challenge to it?

The justified true belief (JTB) account of knowledge purports to give the necessary and sufficient conditions for an subject's having knowledge. Precisely, the account states that a subject S knows a proposition P if and only if the following three conditions are met: (1) S believes that p.(2) S is justified in believing that p.(3) P is true. The JTB account of knowledge is intuitively plausible. It is generally agreed that we can only know a proposition if that proposition is true, that is, we cannot know anything false. It seems intuitive that we can only know a proposition if we believe that proposition. Finally, we tend to think phenomena such as lucky guesses do not amount to knowledge - for a belief to be knowledge it seems we must have reasons or evidence for believing it. The account is put under pressure by Gettier-style cases. Imagine that Smith and Jones have both applied for the same job. The interviewer for the job has informed Smith that Jones will get the job. Moreover, Smith has counted the coins in Jones' pocket, and found that he has ten coins in his pocket. Hence, Smith forms the justified belief (a) that Jones will get the job and Jones has ten coins in his pockets. From this belief he infers and assents to proposition (b): The man who will get the job has ten coins in his pocket. Such inference is justification preserving, and so Smith's belief that (b) is justified. In fact, Smith himself receives the job, and, though he did not know it, he coincidentally has ten coins in his pocket. Therefore, on the JTB account, Smith's belief (b) is knowledge. However, it seems this is not a case of knowledge. Smith's evidence for (b) is not connected to the facts which make (b) true, it is by luck that (b) is true. Hence, (1)-(3) do not provide the sufficient conditions for knowledge, and so the account does not seem to be adequate.