We say $X_{n}$ converges to X in probability if for every $\epsilon$>0, $P\{|X_{n}-X|>\epsilon\}\to 0 \;as\; n \to\infty$
The book I am reading provides the following example to illustrate the joint probability between $X_{n}$ and $X$ must be defined in order to check convergence in probability: $X_{1},X_{2},...$ are i.i.d. normal, $N(0,1)$. Then $X_{n}\to X_{1}$ in distribution but not in probability.
It is not clear to me as to why the joint probability between $X_{n}$ and $X$ must be defined and where it fits in this example.