"Degenerate" in this context means taken to an extreme level so, for example, a straightline is a degenerate version of a triangle. The degenerate baseline hazard seems to me to be one where its obvious given the assumptions and definitions.
$$h_0(t_l|t=s) = {1}/{∑↙{t_j >= t_l} \exp(X_j \beta(s))}$$.
Rearranging this gives
$${∑↙{t_j >= t_l} h_0(t_l|t=s) \exp(X_j \beta(s))}=1$$.
Which says, the sum of the hazards for each case in the risk set just after time $t_l$ (i.e. good as $t_l$ really) is one. By definition there is an event at time $t_l$. We know that there are no ties so there is only one. So, the summation is when there are at least one but no more than one events at time $t_l$. We don't need to consider the cases when there may be more than one event at that time or the probabilities of there not being an event, leaving us with a simple addition.
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