Python – PySpark divides columns by their sums

I’m trying to divide the columns in PySpark by their respective sums. My data frame (using only one column here) looks like this:

event_rates = [[1,10.461016949152542], [2, 10.38953488372093], [3, 10.609418282548477]]
event_rates = spark.createDataFrame(event_rates, ['cluster_id','mean_encoded'])
event_rates.show()

+----------+------------------+
|cluster_id|      mean_encoded|
+----------+------------------+
|         1|10.461016949152542|
|         2| 10.38953488372093|
|         3|10.609418282548477|
+----------+------------------+

I tried both methods to do this, but neither got results

from pyspark.sql.functions import sum as spark_sum
cols = event_rates.columns[1:]
for each in cols:
    event_rates = event_rates.withColumn(each+"_scaled", event_rates[each]/spark_sum(event_rates[each]))

This gives me the following error

org.apache.spark.sql.AnalysisException: grouping expressions sequence is empty, and '`cluster_id`' is not an aggregate function. Wrap '((`mean_encoded` / sum(`mean_encoded`)) AS `mean_encoded_scaled`)' in windowing function(s) or wrap '`cluster_id`' in first() (or first_value) if you don't care which value you get.;;
Aggregate [cluster_id#22356L, mean_encoded#22357, (mean_encoded#22357 / sum(mean_encoded#22357)) AS mean_encoded_scaled#2

and follow the question Here I tried the following

stats = (event_rates.agg([spark_sum(x).alias(x + '_sum') for x in cols]))
event_rates = event_rates.join(broadcast(stats))
exprs = [event_rates[x] / event_rates[event_rates + '_sum'] for x in cols]
event_rates.select(exprs)

But I get an error from the first line

AssertionError: all exprs should be Column

How do I fix this?