I am going to give you a slight python alternative to the other answer. I am not going to write out the whole thing, but if you are familiar with arcpy, you should be able to fill in the gaps.
First things first. Select those Subdivision features that contain and inspection point.
arcpy.SelectLayerByLocation_management("SUBDIVISION", "CONTAINS", "INSPECTION POINT", 0, "NEW_SELECTION")
Now you can go through the selected features and grab the FID information.
First describe the layer to get the selected info.
select = arcpy.Describe("SUBDIVISION")
Now you want to go through the selected features to grab an identifier.
for feature in select.FIDset.split("; "):
#here is where you can use your identifier to build an expression
#I usually have a global variable (ex: expression) where I append values to it
#something like.. myExpression += "FID = '" + feature + "' or "
#without using a sentinel/counter, I end up having to remove the last " or "
#to each his own though.. just giving you ideas
#here I am just printing it though
Now, you need to get the layer you're working with. I am assuming you've got it loaded up in the data frame/Table of Contents.
I select my layer, but I first need to create a map document to use for my function.
mxd = arcpy.mapping.MapDocument("CURRENT")
layer = arcpy.mapping.ListLayers(mxd, "SUBDIVISION*")
#ListLayers returns a list, I am using "SUBDIVISION*" as a wildcard to limit to only the one I want
#results may vary on this though.. it is up to you to make it right
From here, you can edit your labeling expressions. I did that like this.
layer.labelClasses.SQLQuery = myExpression
layer.labelClasses.expression = #field you want to label with (optional)
I am taking the expression I made and using it as a SQL Query against the layer. This sets the selected features that you want to label. Then I am taking the expression part of the labelClass to write out the field I want to label with. This is optional though, the SQL Query is the part that matters, the rest can be done manually. If you look at the properties of the expression and SQLQuery, you can see the code modified those with the layer. Make sure you Method is set to Define classes of fatures and label each differently to see how the default class was edited. I am not 100% sure this works if you have it set as Label all the features the same way.. I know you can't see the SQLQuery part, and I did not fully test this to double check. (Layer Properties -> Labels -> Expression/SQLQuery).
You can modify this to be a cut and paste script you drop in the interactive window (like I did) or make it a tool, if you desire.