Viterbi Algorithm: initial state with ONE probability
Wikipedia is wrong.  That's not what $T_1$ stores.  Rather, $T_1$ stores the likelihood of a path... namely, the likelihood of the path that has the highest likelihood.  What's the likelihood of a path $\hat{X}$?  It is the probability of generating the output sequence $Y$ given that you followed the path $\hat{X}$, i.e., the probability $P(Y | \hat{X})$.  Note that this is not the same as $P(\hat{X} | Y)$.

The probability $P(Y | \hat{X})$ might be less than 1, even if we're certain that $\hat{X}$ was the path that was followed.  In particular, you can have $P(Y | \hat{X}) &lt; 1$ even if $P(\hat{X}) = 1$.  This can happen, for example, if there are multiple possible output sequences that could arise when following the path $\hat{X}$.

As usual, Wikipedia is not a primary source.  Don't use Wikipedia as your only source for learning new material.  It is helpful as a summary, but when you find something in Wikipedia that is confusing or that doesn't make sense, go to a primary source -- e.g., a highly reputed textbook.  Wikipedia does have errors, poor writing, gaps in its explanation, and so on, so it is not a substitute for a high-quality primary source.