Step 1: Understand the concept of basicity.
Basicity refers to the ability of a substance to accept protons (H$^+$) in a chemical reaction. The stronger the base, the more readily it can accept protons.
Step 2: Analyze each option.
- AsH$_3$ (Arsine) is a weaker base because arsenic (As) is less electronegative than phosphorus, so its ability to donate electrons to bond with protons is lower.
- SbH$_3$ (Stibine) is an even weaker base than arsine because antimony (Sb) is even less electronegative than arsenic.
- PH$_3$ (Phosphine) is a weak base because phosphorus is less electronegative than nitrogen, and its lone pair is less available for protonation.
- NH$_3$ (Ammonia) is the strongest base in this group because nitrogen is highly electronegative, making its lone pair more available to bond with protons.
Step 3: Apply to the options.
Ammonia (NH$_3$) is the strongest base among the options due to nitrogen's high electronegativity and its ability to donate its lone pair easily.
Final Answer:
\[
\boxed{\text{NH}_3}
\]